CINXE.COM

<!DOCTYPE html> <html lang="en" xmlns:fb="http://www.facebook.com/2008/fbml" class="wf-loading"> <head prefix="og: https://ogp.me/ns# fb: https://ogp.me/ns/fb# academia: https://ogp.me/ns/fb/academia#"> <meta charset="utf-8"> <meta name=viewport content="width=device-width, initial-scale=1"> <meta rel="search" type="application/opensearchdescription+xml" href="/open_search.xml" title="Academia.edu"> <title>Thomas Schick | Georg-August-Universität Göttingen - Academia.edu</title>  <link href="//a.academia-assets.com/images/favicons/favicon-production.ico" rel="shortcut icon" type="image/vnd.microsoft.icon"> <link rel="apple-touch-icon" sizes="57x57" href="//a.academia-assets.com/images/favicons/apple-touch-icon-57x57.png"> <link rel="apple-touch-icon" sizes="60x60" href="//a.academia-assets.com/images/favicons/apple-touch-icon-60x60.png"> <link rel="apple-touch-icon" sizes="72x72" href="//a.academia-assets.com/images/favicons/apple-touch-icon-72x72.png"> <link rel="apple-touch-icon" sizes="76x76" href="//a.academia-assets.com/images/favicons/apple-touch-icon-76x76.png"> <link rel="apple-touch-icon" sizes="114x114" href="//a.academia-assets.com/images/favicons/apple-touch-icon-114x114.png"> <link rel="apple-touch-icon" sizes="120x120" href="//a.academia-assets.com/images/favicons/apple-touch-icon-120x120.png"> <link rel="apple-touch-icon" sizes="144x144" href="//a.academia-assets.com/images/favicons/apple-touch-icon-144x144.png"> <link rel="apple-touch-icon" sizes="152x152" href="//a.academia-assets.com/images/favicons/apple-touch-icon-152x152.png"> <link rel="apple-touch-icon" sizes="180x180" href="//a.academia-assets.com/images/favicons/apple-touch-icon-180x180.png"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-32x32.png" sizes="32x32"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-194x194.png" sizes="194x194"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-96x96.png" sizes="96x96"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/android-chrome-192x192.png" sizes="192x192"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-16x16.png" sizes="16x16"> <link rel="manifest" href="//a.academia-assets.com/images/favicons/manifest.json"> <meta name="msapplication-TileColor" content="#2b5797"> <meta name="msapplication-TileImage" content="//a.academia-assets.com/images/favicons/mstile-144x144.png"> <meta name="theme-color" content="#ffffff"> <script> window.performance && window.performance.measure && window.performance.measure("Time To First Byte", "requestStart", "responseStart"); </script> <script> (function() { if (!window.URLSearchParams || !window.history || !window.history.replaceState) { return; } var searchParams = new URLSearchParams(window.location.search); var paramsToDelete = [ 'fs', 'sm', 'swp', 'iid', 'nbs', 'rcc', // related content category 'rcpos', // related content carousel position 'rcpg', // related carousel page 'rchid', // related content hit id 'f_ri', // research interest id, for SEO tracking 'f_fri', // featured research interest, for SEO tracking (param key without value) 'f_rid', // from research interest directory for SEO tracking 'f_loswp', // from research interest pills on LOSWP sidebar for SEO tracking 'rhid', // referrring hit id ]; if (paramsToDelete.every((key) => searchParams.get(key) === null)) { return; } paramsToDelete.forEach((key) => { searchParams.delete(key); }); var cleanUrl = new URL(window.location.href); cleanUrl.search = searchParams.toString(); history.replaceState({}, document.title, cleanUrl); })(); </script> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "profiles/works", 'action': "summary", 'controller_action': 'profiles/works#summary', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script type="text/javascript"> window.sendUserTiming = function(timingName) { if (!(window.performance && window.performance.measure)) return; var entries = window.performance.getEntriesByName(timingName, "measure"); if (entries.length !== 1) return; var timingValue = Math.round(entries[0].duration); gtag('event', 'timing_complete', { name: timingName, value: timingValue, event_category: 'User-centric', }); }; window.sendUserTiming("Time To First Byte"); </script> <meta name="csrf-param" content="authenticity_token" /> <meta name="csrf-token" content="s1hMhSQoAvpHDXLFXQpsZ0s-ukp2CNkw-v1KmBAwLugn-yZJcUwQCGGK4y5T2IYvTJ8eFqHtJ1La709FD2IOGg" /> <link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/wow-3d36c19b4875b226bfed0fcba1dcea3f2fe61148383d97c0465c016b8c969290.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/social/home-79e78ce59bef0a338eb6540ec3d93b4a7952115b56c57f1760943128f4544d42.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/heading-95367dc03b794f6737f30123738a886cf53b7a65cdef98a922a98591d60063e3.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/button-bfbac2a470372e2f3a6661a65fa7ff0a0fbf7aa32534d9a831d683d2a6f9e01b.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/body-170d1319f0e354621e81ca17054bb147da2856ec0702fe440a99af314a6338c5.css" /><link crossorigin="" href="https://fonts.gstatic.com/" rel="preconnect" /><link href="https://fonts.googleapis.com/css2?family=DM+Sans:ital,opsz,wght@0,9..40,100..1000;1,9..40,100..1000&family=Gupter:wght@400;500;700&family=IBM+Plex+Mono:wght@300;400&family=Material+Symbols+Outlined:opsz,wght,FILL,GRAD@20,400,0,0&display=swap" rel="stylesheet" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/common-2b6f90dbd75f5941bc38f4ad716615f3ac449e7398313bb3bc225fba451cd9fa.css" /> <meta name="author" content="thomas schick" /> <meta name="description" content="Thomas Schick, Georg-August-Universität Göttingen: 127 Followers, 1 Following, 118 Research papers. Research interests: Algebraic Topology, Topology, and…" /> <meta name="google-site-verification" content="bKJMBZA7E43xhDOopFZkssMMkBRjvYERV-NaN4R6mrs" /> <script> var $controller_name = 'works'; var $action_name = "summary"; var $rails_env = 'production'; var $app_rev = '075e914b9e16164113b5b9afd7238a56a7292942'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.Aedu = { hit_data: null }; window.Aedu.SiteStats = {"premium_universities_count":14035,"monthly_visitors":"102 million","monthly_visitor_count":102864795,"monthly_visitor_count_in_millions":102,"user_count":283263869,"paper_count":55203019,"paper_count_in_millions":55,"page_count":432000000,"page_count_in_millions":432,"pdf_count":16500000,"pdf_count_in_millions":16}; window.Aedu.serverRenderTime = new Date(1740055934000); window.Aedu.timeDifference = new Date().getTime() - 1740055934000; window.Aedu.isUsingCssV1 = false; window.Aedu.enableLocalization = true; window.Aedu.activateFullstory = false; window.Aedu.serviceAvailability = { status: {"attention_db":"on","bibliography_db":"on","contacts_db":"on","email_db":"on","indexability_db":"on","mentions_db":"on","news_db":"on","notifications_db":"on","offsite_mentions_db":"on","redshift":"on","redshift_exports_db":"on","related_works_db":"on","ring_db":"on","user_tests_db":"on"}, serviceEnabled: function(service) { return this.status[service] === "on"; }, readEnabled: function(service) { return this.serviceEnabled(service) || this.status[service] === "read_only"; }, }; window.Aedu.viewApmTrace = function() { // Check if x-apm-trace-id meta tag is set, and open the trace in APM // in a new window if it is. var apmTraceId = document.head.querySelector('meta[name="x-apm-trace-id"]'); if (apmTraceId) { var traceId = apmTraceId.content; // Use trace ID to construct URL, an example URL looks like: // https://app.datadoghq.com/apm/traces?query=trace_id%31298410148923562634 var apmUrl = 'https://app.datadoghq.com/apm/traces?query=trace_id%3A' + traceId; window.open(apmUrl, '_blank'); } }; </script>  <link href="https://fonts.googleapis.com/css?family=Roboto:100,100i,300,300i,400,400i,500,500i,700,700i,900,900i" rel="stylesheet"> <link rel="preload" href="//maxcdn.bootstrapcdn.com/font-awesome/4.3.0/css/font-awesome.min.css" as="style" onload="this.rel='stylesheet'"> <link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/libraries-a9675dcb01ec4ef6aa807ba772c7a5a00c1820d3ff661c1038a20f80d06bb4e4.css" /> <link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/academia-40698df34f913bd208bb70f09d2feb7c6286046250be17a4db35bba2c08b0e2f.css" /> <link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system_legacy-056a9113b9a0f5343d013b29ee1929d5a18be35fdcdceb616600b4db8bd20054.css" /> <script src="//a.academia-assets.com/assets/webpack_bundles/runtime-bundle-005434038af4252ca37c527588411a3d6a0eabb5f727fac83f8bbe7fd88d93bb.js"></script> <script src="//a.academia-assets.com/assets/webpack_bundles/webpack_libraries_and_infrequently_changed.wjs-bundle-6145545f49b709c1199990a76c559bd4c35429284884cbcb3cf7f1916215e941.js"></script> <script src="//a.academia-assets.com/assets/webpack_bundles/core_webpack.wjs-bundle-5e022a2ab081599fcedc76886fa95a606f8073416cae1641695a9906c9a80b81.js"></script> <script src="//a.academia-assets.com/assets/webpack_bundles/sentry.wjs-bundle-5fe03fddca915c8ba0f7edbe64c194308e8ce5abaed7bffe1255ff37549c4808.js"></script> <script> jade = window.jade || {}; jade.helpers = window.$h; jade._ = window._; </script>  <script id="tag-manager-head-root">(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer_old','GTM-5G9JF7Z');</script>  <script> window.gptadslots = []; window.googletag = window.googletag || {}; window.googletag.cmd = window.googletag.cmd || []; </script> <script type="text/javascript"> // TODO(jacob): This should be defined, may be rare load order problem. // Checking if null is just a quick fix, will default to en if unset. // Better fix is to run this immedietely after I18n is set. if (window.I18n != null) { I18n.defaultLocale = "en"; I18n.locale = "en"; I18n.fallbacks = true; } </script> <link rel="canonical" href="https://uni-goettingen.academia.edu/TSchick" /> </head>   <body class='c-profiles/works a-summary logged_out'>  <div id="fb-root"></div><script>window.fbAsyncInit = function() { FB.init({ appId: "2369844204", version: "v8.0", status: true, cookie: true, xfbml: true }); // Additional initialization code. if (window.InitFacebook) { // facebook.ts already loaded, set it up. window.InitFacebook(); } else { // Set a flag for facebook.ts to find when it loads. window.academiaAuthReadyFacebook = true; } };</script><script>window.fbAsyncLoad = function() { // Protection against double calling of this function if (window.FB) { return; } (function(d, s, id){ var js, fjs = d.getElementsByTagName(s)[0]; if (d.getElementById(id)) {return;} js = d.createElement(s); js.id = id; js.src = "//connect.facebook.net/en_US/sdk.js"; fjs.parentNode.insertBefore(js, fjs); }(document, 'script', 'facebook-jssdk')); } if (!window.defer_facebook) { // Autoload if not deferred window.fbAsyncLoad(); } else { // Defer loading by 5 seconds setTimeout(function() { window.fbAsyncLoad(); }, 5000); }</script> <div id="google-root"></div><script>window.loadGoogle = function() { if (window.InitGoogle) { // google.ts already loaded, set it up. window.InitGoogle("331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b"); } else { // Set a flag for google.ts to use when it loads. window.GoogleClientID = "331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b"; } };</script><script>window.googleAsyncLoad = function() { // Protection against double calling of this function (function(d) { var js; var id = 'google-jssdk'; var ref = d.getElementsByTagName('script')[0]; if (d.getElementById(id)) { return; } js = d.createElement('script'); js.id = id; js.async = true; js.onload = loadGoogle; js.src = "https://accounts.google.com/gsi/client" ref.parentNode.insertBefore(js, ref); }(document)); } if (!window.defer_google) { // Autoload if not deferred window.googleAsyncLoad(); } else { // Defer loading by 5 seconds setTimeout(function() { window.googleAsyncLoad(); }, 5000); }</script> <div id="tag-manager-body-root">  <noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-5G9JF7Z" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>   <script> window.addEventListener('load', function() { if (document.querySelector('input[name="commit"]')) { document.querySelector('input[name="commit"]').addEventListener('click', function() { gtag('event', 'click', { event_category: 'button', event_label: 'Log In' }) }) } }); </script> </div> <script>var _comscore = _comscore || []; _comscore.push({ c1: "2", c2: "26766707" }); (function() { var s = document.createElement("script"), el = document.getElementsByTagName("script")[0]; s.async = true; s.src = (document.location.protocol == "https:" ? "https://sb" : "http://b") + ".scorecardresearch.com/beacon.js"; el.parentNode.insertBefore(s, el); })();</script><img src="https://sb.scorecardresearch.com/p?c1=2&c2=26766707&cv=2.0&cj=1" style="position: absolute; visibility: hidden" /> <div id='react-modal'></div> <div class='DesignSystem'> <a class='u-showOnFocus' href='#site'> Skip to main content </a> </div> <div id="upgrade_ie_banner" style="display: none;"><p>Academia.edu no longer supports Internet Explorer.</p><p>To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to <a href="https://www.academia.edu/upgrade-browser">upgrade your browser</a>.</p></div><script>// Show this banner for all versions of IE if (!!window.MSInputMethodContext || /(MSIE)/.test(navigator.userAgent)) { document.getElementById('upgrade_ie_banner').style.display = 'block'; }</script> <div class="DesignSystem bootstrap ShrinkableNav"><div class="navbar navbar-default main-header"><div class="container-wrapper" id="main-header-container"><div class="container"><div class="navbar-header"><div class="nav-left-wrapper u-mt0x"><div class="nav-logo"><a data-main-header-link-target="logo_home" href="https://www.academia.edu/"><img class="visible-xs-inline-block" style="height: 24px;" alt="Academia.edu" src="//a.academia-assets.com/images/academia-logo-redesign-2015-A.svg" width="24" height="24" /><img width="145.2" height="18" class="hidden-xs" style="height: 24px;" alt="Academia.edu" src="//a.academia-assets.com/images/academia-logo-redesign-2015.svg" /></a></div><div class="nav-search"><div class="SiteSearch-wrapper select2-no-default-pills"><form class="js-SiteSearch-form DesignSystem" action="https://www.academia.edu/search" accept-charset="UTF-8" method="get"><i class="SiteSearch-icon fa fa-search u-fw700 u-positionAbsolute u-tcGrayDark"></i><input class="js-SiteSearch-form-input SiteSearch-form-input form-control" data-main-header-click-target="search_input" name="q" placeholder="Search" type="text" value="" /></form></div></div></div><div class="nav-right-wrapper pull-right"><ul class="NavLinks js-main-nav list-unstyled"><li class="NavLinks-link"><a class="js-header-login-url Button Button--inverseGray Button--sm u-mb4x" id="nav_log_in" rel="nofollow" href="https://www.academia.edu/login">Log In</a></li><li class="NavLinks-link u-p0x"><a class="Button Button--inverseGray Button--sm u-mb4x" rel="nofollow" href="https://www.academia.edu/signup">Sign Up</a></li></ul><button class="hidden-lg hidden-md hidden-sm u-ml4x navbar-toggle collapsed" data-target=".js-mobile-header-links" data-toggle="collapse" type="button"><span class="icon-bar"></span><span class="icon-bar"></span><span class="icon-bar"></span></button></div></div><div class="collapse navbar-collapse js-mobile-header-links"><ul class="nav navbar-nav"><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/login">Log In</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/signup">Sign Up</a></li><li class="u-borderColorGrayLight u-borderBottom1 js-mobile-nav-expand-trigger"><a href="#">more&nbsp<span class="caret"></span></a></li><li><ul class="js-mobile-nav-expand-section nav navbar-nav u-m0x collapse"><li class="u-borderColorGrayLight u-borderBottom1"><a rel="false" href="https://www.academia.edu/about">About</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/press">Press</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="false" href="https://www.academia.edu/documents">Papers</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/terms">Terms</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/privacy">Privacy</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/copyright">Copyright</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/hiring"><i class="fa fa-briefcase"></i> We're Hiring!</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://support.academia.edu/hc/en-us"><i class="fa fa-question-circle"></i> Help Center</a></li><li class="js-mobile-nav-collapse-trigger u-borderColorGrayLight u-borderBottom1 dropup" style="display:none"><a href="#">less&nbsp<span class="caret"></span></a></li></ul></li></ul></div></div></div><script>(function(){ var $moreLink = $(".js-mobile-nav-expand-trigger"); var $lessLink = $(".js-mobile-nav-collapse-trigger"); var $section = $('.js-mobile-nav-expand-section'); $moreLink.click(function(ev){ ev.preventDefault(); $moreLink.hide(); $lessLink.show(); $section.collapse('show'); }); $lessLink.click(function(ev){ ev.preventDefault(); $moreLink.show(); $lessLink.hide(); $section.collapse('hide'); }); })() if ($a.is_logged_in() || false) { new Aedu.NavigationController({ el: '.js-main-nav', showHighlightedNotification: false }); } else { $(".js-header-login-url").attr("href", $a.loginUrlWithRedirect()); } Aedu.autocompleteSearch = new AutocompleteSearch({el: '.js-SiteSearch-form'});</script></div></div> <div id='site' class='fixed'> <div id="content" class="clearfix"> <script>document.addEventListener('DOMContentLoaded', function(){ var $dismissible = $(".dismissible_banner"); $dismissible.click(function(ev) { $dismissible.hide(); }); });</script> <script src="//a.academia-assets.com/assets/webpack_bundles/profile.wjs-bundle-8e43dbfb783947b05fb193bb4a981fdefb46b9285b0cade100b20d38357a3356.js" defer="defer"></script><script>$viewedUser = Aedu.User.set_viewed( {"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick","photo":"https://0.academia-photos.com/35644036/10332640/11530375/s65_t..schick.jpg","has_photo":true,"department":{"id":11105,"name":"Mathematisches Institut","url":"https://uni-goettingen.academia.edu/Departments/Mathematisches_Institut/Documents","university":{"id":1327,"name":"Georg-August-Universität Göttingen","url":"https://uni-goettingen.academia.edu/"}},"position":"Faculty Member","position_id":1,"is_analytics_public":false,"interests":[{"id":6296,"name":"Algebraic Topology","url":"https://www.academia.edu/Documents/in/Algebraic_Topology"},{"id":15118,"name":"Topology","url":"https://www.academia.edu/Documents/in/Topology"},{"id":2890,"name":"Operator Algebras","url":"https://www.academia.edu/Documents/in/Operator_Algebras"},{"id":2336,"name":"Homotopy Theory","url":"https://www.academia.edu/Documents/in/Homotopy_Theory"},{"id":97187,"name":"C*-algebras","url":"https://www.academia.edu/Documents/in/C_-algebras"}]} ); if ($a.is_logged_in() && $viewedUser.is_current_user()) { $('body').addClass('profile-viewed-by-owner'); } $socialProfiles = []</script><div id="js-react-on-rails-context" style="display:none" data-rails-context="{"inMailer":false,"i18nLocale":"en","i18nDefaultLocale":"en","href":"https://uni-goettingen.academia.edu/TSchick","location":"/TSchick","scheme":"https","host":"uni-goettingen.academia.edu","port":null,"pathname":"/TSchick","search":null,"httpAcceptLanguage":null,"serverSide":false}"></div> <div class="js-react-on-rails-component" style="display:none" data-component-name="ProfileCheckPaperUpdate" data-props="{}" data-trace="false" data-dom-id="ProfileCheckPaperUpdate-react-component-9f10c5ff-fcbf-4c4c-a0cd-658963587fe5"></div> <div id="ProfileCheckPaperUpdate-react-component-9f10c5ff-fcbf-4c4c-a0cd-658963587fe5"></div> <div class="DesignSystem"><div class="onsite-ping" id="onsite-ping"></div></div><div class="profile-user-info DesignSystem"><div class="social-profile-container"><div class="left-panel-container"><div class="user-info-component-wrapper"><div class="user-summary-cta-container"><div class="user-summary-container"><div class="social-profile-avatar-container"><img class="profile-avatar u-positionAbsolute" alt="Thomas Schick" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/35644036/10332640/11530375/s200_t..schick.jpg" /></div><div class="title-container"><h1 class="ds2-5-heading-sans-serif-sm">Thomas Schick</h1><div class="affiliations-container fake-truncate js-profile-affiliations"><div><a class="u-tcGrayDarker" href="https://uni-goettingen.academia.edu/">Georg-August-Universität Göttingen</a>, <a class="u-tcGrayDarker" href="https://uni-goettingen.academia.edu/Departments/Mathematisches_Institut/Documents">Mathematisches Institut</a>, <span class="u-tcGrayDarker">Faculty Member</span></div></div></div></div><div class="sidebar-cta-container"><button class="ds2-5-button hidden profile-cta-button grow js-profile-follow-button" data-broccoli-component="user-info.follow-button" data-click-track="profile-user-info-follow-button" data-follow-user-fname="Thomas" data-follow-user-id="35644036" data-follow-user-source="profile_button" data-has-google="false"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">add</span>Follow</button><button class="ds2-5-button hidden profile-cta-button grow js-profile-unfollow-button" data-broccoli-component="user-info.unfollow-button" data-click-track="profile-user-info-unfollow-button" data-unfollow-user-id="35644036"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">done</span>Following</button></div></div><div class="user-stats-container"><a><div class="stat-container js-profile-followers"><p class="label">Followers</p><p class="data">127</p></div></a><a><div class="stat-container js-profile-followees" data-broccoli-component="user-info.followees-count" data-click-track="profile-expand-user-info-following"><p class="label">Following</p><p class="data">1</p></div></a><a><div class="stat-container js-profile-coauthors" data-broccoli-component="user-info.coauthors-count" data-click-track="profile-expand-user-info-coauthors"><p class="label">Co-author</p><p class="data">1</p></div></a><div class="js-mentions-count-container" style="display: none;"><a href="/TSchick/mentions"><div class="stat-container"><p class="label">Mentions</p><p class="data"></p></div></a></div><span><div class="stat-container"><p class="label"><span class="js-profile-total-view-text">Public Views</span></p><p class="data"><span class="js-profile-view-count"></span></p></div></span></div><div class="suggested-academics-container"><div class="suggested-academics--header"><p class="ds2-5-body-md-bold">Related Authors</p></div><ul class="suggested-user-card-list"><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://valdosta.academia.edu/ShaunAult"><img class="profile-avatar u-positionAbsolute" alt="Shaun V Ault" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/27428/8957/3424372/s200_shaun.ault.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://valdosta.academia.edu/ShaunAult">Shaun V Ault</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Valdosta State University</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://ksu.academia.edu/DavidSeamon"><img class="profile-avatar u-positionAbsolute" alt="David Seamon" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/93547/25922/29662134/s200_david.seamon.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://ksu.academia.edu/DavidSeamon">David Seamon</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Kansas State University</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://wur.academia.edu/VincentBlok"><img class="profile-avatar u-positionAbsolute" alt="Vincent Blok" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/110734/432961/5476864/s200_vincent.blok.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://wur.academia.edu/VincentBlok">Vincent Blok</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Wageningen University</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://cria.academia.edu/ArmandoMarquesGuedes"><img class="profile-avatar u-positionAbsolute" alt="Armando Marques-Guedes" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/134181/3401094/148494125/s200_armando.marques-guedes.png" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://cria.academia.edu/ArmandoMarquesGuedes">Armando Marques-Guedes</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">UNL - New University of Lisbon</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://unilorin.academia.edu/FadipeJosephOlubunmi"><img class="profile-avatar u-positionAbsolute" alt="Fadipe-Joseph Olubunmi" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/148366/21739704/21053013/s200_fadipe-joseph.olubunmi.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://unilorin.academia.edu/FadipeJosephOlubunmi">Fadipe-Joseph Olubunmi</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">University of Ilorin</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://uci.academia.edu/ManuelReyes"><img class="profile-avatar u-positionAbsolute" alt="Manuel Reyes" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/245062/3209160/4103957/s200_manuel.reyes.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://uci.academia.edu/ManuelReyes">Manuel Reyes</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">University of California, Irvine</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://hacettepe.academia.edu/U%C4%9FurG%C3%BCl"><img class="profile-avatar u-positionAbsolute" alt="Uğur Gül" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/1375299/3785046/21026028/s200_u_ur.g_l.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://hacettepe.academia.edu/U%C4%9FurG%C3%BCl">Uğur Gül</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Hacettepe University</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://ucla.academia.edu/NinaOtter"><img class="profile-avatar u-positionAbsolute" alt="Nina Otter" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/4749551/2013811/18582555/s200_nina.otter.png" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://ucla.academia.edu/NinaOtter">Nina Otter</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">University of California, Los Angeles</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://neu.academia.edu/AlexSuciu"><img class="profile-avatar u-positionAbsolute" alt="Alex Suciu" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/6493129/3748567/4390929/s200_alex.suciu.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://neu.academia.edu/AlexSuciu">Alex Suciu</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Northeastern University</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://yildiz.academia.edu/NasreenKausar"><img class="profile-avatar u-positionAbsolute" alt="Nasreen Kausar" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/29298824/8376101/32886878/s200_nasreen.kausar.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://yildiz.academia.edu/NasreenKausar">Nasreen Kausar</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Yildiz Technical University</p></div></div></ul></div><div class="ri-section"><div class="ri-section-header"><span>Interests</span></div><div class="ri-tags-container"><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="35644036" href="https://www.academia.edu/Documents/in/Algebraic_Topology"><div id="js-react-on-rails-context" style="display:none" data-rails-context="{"inMailer":false,"i18nLocale":"en","i18nDefaultLocale":"en","href":"https://uni-goettingen.academia.edu/TSchick","location":"/TSchick","scheme":"https","host":"uni-goettingen.academia.edu","port":null,"pathname":"/TSchick","search":null,"httpAcceptLanguage":null,"serverSide":false}"></div> <div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Algebraic Topology"]}" data-trace="false" data-dom-id="Pill-react-component-897b223d-cb6c-4dfd-912e-bb53cdd16c9b"></div> <div id="Pill-react-component-897b223d-cb6c-4dfd-912e-bb53cdd16c9b"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="35644036" href="https://www.academia.edu/Documents/in/Topology"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Topology"]}" data-trace="false" data-dom-id="Pill-react-component-c030e1b4-6272-4d60-8af3-19069311018f"></div> <div id="Pill-react-component-c030e1b4-6272-4d60-8af3-19069311018f"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="35644036" href="https://www.academia.edu/Documents/in/Operator_Algebras"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Operator Algebras"]}" data-trace="false" data-dom-id="Pill-react-component-90fe768c-d863-4b4c-9166-c61e634a1db1"></div> <div id="Pill-react-component-90fe768c-d863-4b4c-9166-c61e634a1db1"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="35644036" href="https://www.academia.edu/Documents/in/Homotopy_Theory"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Homotopy Theory"]}" data-trace="false" data-dom-id="Pill-react-component-f7736a85-23ac-4c87-81a2-b1491040e652"></div> <div id="Pill-react-component-f7736a85-23ac-4c87-81a2-b1491040e652"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="35644036" href="https://www.academia.edu/Documents/in/C_-algebras"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["C*-algebras"]}" data-trace="false" data-dom-id="Pill-react-component-e6ba3073-11a2-43e6-8da1-2c436fe04985"></div> <div id="Pill-react-component-e6ba3073-11a2-43e6-8da1-2c436fe04985"></div> </a></div></div></div></div><div class="right-panel-container"><div class="user-content-wrapper"><div class="uploads-container" id="social-redesign-work-container"><div class="upload-header"><h2 class="ds2-5-heading-sans-serif-xs">Uploads</h2></div><div class="documents-container backbone-social-profile-documents" style="width: 100%;"><div class="u-taCenter"></div><div class="profile--tab_content_container js-tab-pane tab-pane active" id="all"><div class="profile--tab_heading_container js-section-heading" data-section="Papers" id="Papers"><h3 class="profile--tab_heading_container">Papers by Thomas Schick</h3></div><div class="js-work-strip profile--work_container" data-work-id="20923975"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/20923975/Analysis_on_manifolds_of_bounded_geometry_Hodge_De_Rham_isomorphism_and_L_2_index_theorem"><img alt="Research paper thumbnail of Analysis on ∂-manifolds of bounded geometry, Hodge-De Rham isomorphism and L[2]-index theorem" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/20923975/Analysis_on_manifolds_of_bounded_geometry_Hodge_De_Rham_isomorphism_and_L_2_index_theorem">Analysis on ∂-manifolds of bounded geometry, Hodge-De Rham isomorphism and L[2]-index theorem</a></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923975"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923975"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923975; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923975]").text(description); $(".js-view-count[data-work-id=20923975]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923975; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923975']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=20923975]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923975,"title":"Analysis on ∂-manifolds of bounded geometry, Hodge-De Rham isomorphism and L[2]-index theorem","internal_url":"https://www.academia.edu/20923975/Analysis_on_manifolds_of_bounded_geometry_Hodge_De_Rham_isomorphism_and_L_2_index_theorem","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923973"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/20923973/Modern_index_Theory_lectures_held_at_CIRM_rencontre_Theorie_dindice_Mar_2006"><img alt="Research paper thumbnail of Modern index Theory — lectures held at CIRM rencontre "Theorie d'indice", Mar 2006" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/20923973/Modern_index_Theory_lectures_held_at_CIRM_rencontre_Theorie_dindice_Mar_2006">Modern index Theory — lectures held at CIRM rencontre "Theorie d'indice", Mar 2006</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923973"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923973"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923973; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923973]").text(description); $(".js-view-count[data-work-id=20923973]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923973; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923973']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=20923973]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923973,"title":"Modern index Theory — lectures held at CIRM rencontre \"Theorie d'indice\", Mar 2006","internal_url":"https://www.academia.edu/20923973/Modern_index_Theory_lectures_held_at_CIRM_rencontre_Theorie_dindice_Mar_2006","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923967"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923967/A_counterexample_to_a_conjecture_about_positive_scalar_curvature"><img alt="Research paper thumbnail of A counterexample to a conjecture about positive scalar curvature" class="work-thumbnail" src="https://attachments.academia-assets.com/41630683/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923967/A_counterexample_to_a_conjecture_about_positive_scalar_curvature">A counterexample to a conjecture about positive scalar curvature</a></div><div class="wp-workCard_item"><span>Proceedings of the American Mathematical Society</span><span>, 2015</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">1, Conjecture 1] asserts that a closed smooth manifold M with non-spin universal covering admits ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">1, Conjecture 1] asserts that a closed smooth manifold M with non-spin universal covering admits a metric of positive scalar curvature if and only if a certain homological condition is satisfied. We present a counterexample to this conjecture, based on the counterexample to the unstable Gromov-Lawson-Rosenberg conjecture given in .</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="3bd0b7f09816e4417c01bf40cd197abe" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630683,"asset_id":20923967,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630683/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923967"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923967"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923967; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923967]").text(description); $(".js-view-count[data-work-id=20923967]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923967; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923967']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "3bd0b7f09816e4417c01bf40cd197abe" } } $('.js-work-strip[data-work-id=20923967]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923967,"title":"A counterexample to a conjecture about positive scalar curvature","internal_url":"https://www.academia.edu/20923967/A_counterexample_to_a_conjecture_about_positive_scalar_curvature","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630683,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630683/thumbnails/1.jpg","file_name":"A_Counterexample_to_a_Conjecture_about_P20160127-10948-3yfu5g.pdf","download_url":"https://www.academia.edu/attachments/41630683/download_file","bulk_download_file_name":"A_counterexample_to_a_conjecture_about_p.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630683/A_Counterexample_to_a_Conjecture_about_P20160127-10948-3yfu5g-libre.pdf?1453898566=\u0026response-content-disposition=attachment%3B+filename%3DA_counterexample_to_a_conjecture_about_p.pdf\u0026Expires=1740059534\u0026Signature=N8ZGZbqds9OecywVbLTM3pxSgaGXRgYjC6mCVhvPWhD90DsPfStviNsTaFeABjCviQFhaPNIsKDxHdPkKhj6VOhDmCXL8sWSsfTen2sa6bOcrX3XJCSDNwheMqztQ1FFw27h8Q2~6-DMycm0bwaVGlk97Efi2AEwE1qT6UleTPJU7fQnGAQ-gz1v38QIOJ~Ixo1~8oM-49PszgNInDvU9Z1NjlIkT8STc4NKiN2GET3iKg2hptCHbUCaqkYaGi9VlXewNnAP1b4NsrH9gi3xe~~alfj8CRWdhLq25AQAacu-YR~Ws9xPqJP5~34CFHICm0lK2K3oP1MLBNieC9AZzw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923966"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923966/Codimension_two_index_obstructions_to_positive_scalar_curvature"><img alt="Research paper thumbnail of Codimension two index obstructions to positive scalar curvature" class="work-thumbnail" src="https://attachments.academia-assets.com/41630686/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923966/Codimension_two_index_obstructions_to_positive_scalar_curvature">Codimension two index obstructions to positive scalar curvature</a></div><div class="wp-workCard_item"><span>Annales de l’institut Fourier</span><span>, 2015</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The main result of this paper is a gneral obstruction to the existence of a metric of positive sc...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The main result of this paper is a gneral obstruction to the existence of a metric of positive scalar curvature on a compact spin manifold, given by hypersurfaces of codimension 2. The proof is based on the applicatoin of coarse indes theory to Dirac operatrs twisted by Hilbert C * -module bundles.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="701c89ff7b51464a79dd5e15d4308659" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630686,"asset_id":20923966,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630686/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923966"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923966"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923966; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923966]").text(description); $(".js-view-count[data-work-id=20923966]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923966; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923966']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "701c89ff7b51464a79dd5e15d4308659" } } $('.js-work-strip[data-work-id=20923966]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923966,"title":"Codimension two index obstructions to positive scalar curvature","internal_url":"https://www.academia.edu/20923966/Codimension_two_index_obstructions_to_positive_scalar_curvature","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630686,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630686/thumbnails/1.jpg","file_name":"Codimension_two_index_obstructions_to_po20160127-20216-1dhxq3d.pdf","download_url":"https://www.academia.edu/attachments/41630686/download_file","bulk_download_file_name":"Codimension_two_index_obstructions_to_po.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630686/Codimension_two_index_obstructions_to_po20160127-20216-1dhxq3d-libre.pdf?1453898574=\u0026response-content-disposition=attachment%3B+filename%3DCodimension_two_index_obstructions_to_po.pdf\u0026Expires=1740059534\u0026Signature=QP5rIlnZ00Ee~B6JQk3dYNjZ1yK9seQtaoiql0GRxUQEP4tUgCUjX6hjfQwb1-YgJyWEBvIu74a1evs9-W3PAvD8jIkJVbe0LoYAENT7CRZrtZc2G7QmICxGy64E1a-yBsw5mEDyd4y3mHwJI0xN3k1YRB85-Nu2zqPGNpYM2ZgLVILCETKnbNflg~GPE5mQMJHG-Xo36J~nsuBCoMgF2Nx6yt92HbPYd4rNIvx9HYD3-y3wxrFPpmxhn8ZJGexMek9q~qUhnrEPyeCWCXTHMwbM2zDO4dHv9ecg670E4aglwHW0Ji5hyfFWWGel2NzcA91Gr1d9L91cyYOyB2E4Fw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923965"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923965/The_surgery_exact_sequence_K_theory_and_the_signature_operator"><img alt="Research paper thumbnail of The surgery exact sequence, K-theory and the signature operator" class="work-thumbnail" src="https://attachments.academia-assets.com/41630690/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923965/The_surgery_exact_sequence_K_theory_and_the_signature_operator">The surgery exact sequence, K-theory and the signature operator</a></div><div class="wp-workCard_item"><span>Annals of K-Theory</span><span>, 2016</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper, we study the space of metrics of positive scalar curvature using methods from coar...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper, we study the space of metrics of positive scalar curvature using methods from coarse geometry.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="c39bba77aca27dd494a7672f4dafbe95" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630690,"asset_id":20923965,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630690/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923965"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923965"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923965; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923965]").text(description); $(".js-view-count[data-work-id=20923965]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923965; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923965']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "c39bba77aca27dd494a7672f4dafbe95" } } $('.js-work-strip[data-work-id=20923965]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923965,"title":"The surgery exact sequence, K-theory and the signature operator","internal_url":"https://www.academia.edu/20923965/The_surgery_exact_sequence_K_theory_and_the_signature_operator","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630690,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630690/thumbnails/1.jpg","file_name":"The_surgery_exact_sequence_K-theory_and_20160127-16059-mbickj.pdf","download_url":"https://www.academia.edu/attachments/41630690/download_file","bulk_download_file_name":"The_surgery_exact_sequence_K_theory_and.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630690/The_surgery_exact_sequence_K-theory_and_20160127-16059-mbickj-libre.pdf?1453898578=\u0026response-content-disposition=attachment%3B+filename%3DThe_surgery_exact_sequence_K_theory_and.pdf\u0026Expires=1740046991\u0026Signature=U9sfUYTaqLipjE4qAB5dJCmDuXwnequwJ9fPD2VgklLQ7RZScNmkMmxQN2yfS-5eGRJE8~ZSz17mw6Vd9GMMNc8OD9Bzjdcs5ou7pNOl9jNb3VmNPNhY-6455JJigMqcEtYAANuxsTp7gEXLz0mqZLCHZXEpslhZIALzPgP-oDaDRyhr7OdDq7avZZy72Jqr4bEnNCde0nml94aS4-hJOysQcN98-CgX8h4k1IvrywtnKNgZ1fu8B3BgcrJ0BhRbwTZ9f1Ph8mqM2NpuILACYoKEzkTPa9mCYK~2HMK8npAGqmuiUiMxreIbS1jg2xRVeER5tK0P7c9uLgWByes-7w__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923963"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923963/L_2_index_theorem_for_elliptic_differential_boundary_problems"><img alt="Research paper thumbnail of L 2 -index theorem for elliptic differential boundary problems" class="work-thumbnail" src="https://attachments.academia-assets.com/41630689/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923963/L_2_index_theorem_for_elliptic_differential_boundary_problems">L 2 -index theorem for elliptic differential boundary problems</a></div><div class="wp-workCard_item"><span>Pacific Journal of Mathematics</span><span>, 2001</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Suppose M is a compact manifold with boundary ∂M . Let M ↓M be a normal covering with covering gr...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Suppose M is a compact manifold with boundary ∂M . Let M ↓M be a normal covering with covering group Γ. Suppose (A, T ) is an elliptic differential boundary value problem on M with lift (Ã,T ) toM . Then the von Neumann dimension dim Γ of kernel and cokernel of this lift are defined. The main result of this paper is: these numbers are finite, and their difference, by definition the von Neumann index ind Γ (Ã,T ), equals the index of (A, T ). In this way, we extend the classical L 2 -index theorem of Atiyah to manifolds with boundary.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="573b642c81dca23d4b8e4a1874b93224" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630689,"asset_id":20923963,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630689/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923963"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923963"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923963; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923963]").text(description); $(".js-view-count[data-work-id=20923963]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923963; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923963']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "573b642c81dca23d4b8e4a1874b93224" } } $('.js-work-strip[data-work-id=20923963]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923963,"title":"L 2 -index theorem for elliptic differential boundary problems","internal_url":"https://www.academia.edu/20923963/L_2_index_theorem_for_elliptic_differential_boundary_problems","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630689,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630689/thumbnails/1.jpg","file_name":"L2-index_theorem_for_elliptic_differenti20160127-16059-9k37jf.pdf","download_url":"https://www.academia.edu/attachments/41630689/download_file","bulk_download_file_name":"L_2_index_theorem_for_elliptic_different.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630689/L2-index_theorem_for_elliptic_differenti20160127-16059-9k37jf-libre.pdf?1453898567=\u0026response-content-disposition=attachment%3B+filename%3DL_2_index_theorem_for_elliptic_different.pdf\u0026Expires=1740059534\u0026Signature=FdOKTRzSAtQN1VzECdlgp3RdcwJbjPZls3hi8XDeL9oJ1QRMqtmsZJ9zaSvWcipP3slzKWfl7u6FAO5dXrsdqHX2WPc140WSFZDECSvA1C4L6EiWtiJ7ZKjNpUgeizy5BWZwcrmMPBQ6ClCORP31mTfRsbKf3iFv2R6y0U1iM6JezJpc1TepiQ7rzHHksks01vODJYVCvVu6YGDIbaWugyTXInqSwVMXVk2zfmc3p6e-c21UuOuyMs9CQaBInSjpAl8RjIoV7wDaYa5oze4-3yV4yz8Pyad9YLfBXrLE4hou9-VHJaVlnQ7Zek~uEZwRxze5WKC3RgiORSpCFMddUw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923962"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923962/On_a_conjecture_of_Daniel_H_Gottlieb"><img alt="Research paper thumbnail of On a conjecture of Daniel H. Gottlieb" class="work-thumbnail" src="https://attachments.academia-assets.com/41630678/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923962/On_a_conjecture_of_Daniel_H_Gottlieb">On a conjecture of Daniel H. Gottlieb</a></div><div class="wp-workCard_item"><span>Eprint Arxiv Math 0702826</span><span>, Feb 1, 2007</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We give a counterexample to a conjecture of D.H. Gottlieb and prove a strengthened version of it....</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We give a counterexample to a conjecture of D.H. Gottlieb and prove a strengthened version of it. The conjecture says that a map from a finite CW-complex X to an aspherical CW-complex Y with non-zero Euler characteristic can have non-trivial degree (suitably defined) only if the centralizer of the image of the fundamental group of X is trivial. As a corollary we show that in the above situation all components of non-zero degree maps in the space of maps from X to Y are contractible.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="8f9987ececc5da7eba31813eb08b7217" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630678,"asset_id":20923962,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630678/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923962"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923962"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923962; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923962]").text(description); $(".js-view-count[data-work-id=20923962]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923962; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923962']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "8f9987ececc5da7eba31813eb08b7217" } } $('.js-work-strip[data-work-id=20923962]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923962,"title":"On a conjecture of Daniel H. Gottlieb","internal_url":"https://www.academia.edu/20923962/On_a_conjecture_of_Daniel_H_Gottlieb","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630678,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630678/thumbnails/1.jpg","file_name":"0702826.pdf","download_url":"https://www.academia.edu/attachments/41630678/download_file","bulk_download_file_name":"On_a_conjecture_of_Daniel_H_Gottlieb.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630678/0702826-libre.pdf?1453898567=\u0026response-content-disposition=attachment%3B+filename%3DOn_a_conjecture_of_Daniel_H_Gottlieb.pdf\u0026Expires=1740059534\u0026Signature=Pl7bCkxo80OP~5jlrHx0NvHZdgL3paOoVdYXD9H3vGU6cHtpVbq6NzBZEH8EIcreHEBTGw9wKHE5Kj4MKHkCxFafjbliNprpTpIYEKEIlZkqSUBRXGHO1jvSaYFjGX4ioSqXMZgd~ybQhxRKfV3yUm64taLQRVwbZV6eMBqmcyUkwkYsDPJYyEVjYe9svQI3Qopc2fl43I4-voXoeJiComz2DJnGU~imx~Er3~8Ko2T6cINwAuogNPZngrJZZIsYClaNE6Xw43Z~lbSG8q9AsJuJiddOhol-xZtNth5zqabZpNaqPtgTdKCebm9X6UK4IdSPPE5pkrsJVaddXh~z8A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923961"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923961/A_Model_for_the_Universal_Space_for_Proper_Actions_of_a_Hyperbolic_Group"><img alt="Research paper thumbnail of A Model for the Universal Space for Proper Actions of a Hyperbolic Group" class="work-thumbnail" src="https://attachments.academia-assets.com/41630681/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923961/A_Model_for_the_Universal_Space_for_Proper_Actions_of_a_Hyperbolic_Group">A Model for the Universal Space for Proper Actions of a Hyperbolic Group</a></div><div class="wp-workCard_item"><span>New York Journal of Mathematics</span><span>, Sep 13, 2002</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let $G$ be a word hyperbolic group in the sense of Gromov and $P$ its associated Rips complex. We...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let $G$ be a word hyperbolic group in the sense of Gromov and $P$ its associated Rips complex. We prove that the fixed point set $P^H$ is contractible for every finite subgroups $H$ of $G$. This is the main ingredient for proving that $P$ is a finite model for the universal space $e.g.$ of proper actions. As a corollary we get that a hyperbolic group has only finitely many conjugacy classes of finite subgroups.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="8abc73bbafefea67e09d3df6941265f3" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630681,"asset_id":20923961,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630681/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923961"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923961"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923961; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923961]").text(description); $(".js-view-count[data-work-id=20923961]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923961; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923961']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "8abc73bbafefea67e09d3df6941265f3" } } $('.js-work-strip[data-work-id=20923961]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923961,"title":"A Model for the Universal Space for Proper Actions of a Hyperbolic Group","internal_url":"https://www.academia.edu/20923961/A_Model_for_the_Universal_Space_for_Proper_Actions_of_a_Hyperbolic_Group","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630681,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630681/thumbnails/1.jpg","file_name":"A_Model_for_the_Universal_Space_for_Prop20160127-16054-1bfjnhk.pdf","download_url":"https://www.academia.edu/attachments/41630681/download_file","bulk_download_file_name":"A_Model_for_the_Universal_Space_for_Prop.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630681/A_Model_for_the_Universal_Space_for_Prop20160127-16054-1bfjnhk-libre.pdf?1453898567=\u0026response-content-disposition=attachment%3B+filename%3DA_Model_for_the_Universal_Space_for_Prop.pdf\u0026Expires=1740059534\u0026Signature=dSDQMztua8W8TkA4nLwSM9r8axtI69CPNL-ZBl7bYpJFXeKbwLbWAs7w8p8BNF2xUz6zE4kv7UqJuQlOk0doN4tBSj1XgmlkaDwsvokUlnCqtZGxI~uRNDbnTR47a-dKTXV9hWH3oYMAmUh-0DgBi4g2AiBT~1qEsffT0RL--WtIiKvMdMdo1q3JnVQkYSxdnImKOrpOQ1ubcauO~029Fk2F3I42n6fzbL8O8Mb~U7bJYH152BPCFDmZ98nuQrUXyvFMFVed7iN-gWL0DLVbM3VXNOWu~Xesamhmr6HAAqLkJ2v0JIr6WVr5fCl76QtHnncER-fSE276dNZxgPZqMQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923960"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923960/Quasi_multipliers_of_Hilbert_and_Banach_C_bimodules"><img alt="Research paper thumbnail of Quasi-multipliers of Hilbert and Banach C*-bimodules" class="work-thumbnail" src="https://attachments.academia-assets.com/41630572/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923960/Quasi_multipliers_of_Hilbert_and_Banach_C_bimodules">Quasi-multipliers of Hilbert and Banach C*-bimodules</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Quasi-multipliers for a Hilbert C*-bimodule V were introduced by Brown, Mingo and Shen 1994 as a ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Quasi-multipliers for a Hilbert C*-bimodule V were introduced by Brown, Mingo and Shen 1994 as a certain subset of the Banach bidual module V**. We give another (equivalent) definition of quasi-multipliers for Hilbert C*-bimodules using the centralizer approach and then show that quasi-multipliers are, in fact, universal (maximal) objects of a certain category. We also introduce quasi-multipliers for bimodules in Kasparov's sense and even for Banach bimodules over C*-algebras, provided these C*-algebras act non-degenerately. A topological picture of quasi-multipliers via the quasi-strict topology is given. Finally, we describe quasi-multipliers in two main situations: for the standard Hilbert bimodule l_2(A) and for bimodules of sections of Hilbert C*-bimodule bundles over locally compact spaces.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="5afc0fb53ba036cec066617a86cf551a" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630572,"asset_id":20923960,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630572/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923960"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923960"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923960; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923960]").text(description); $(".js-view-count[data-work-id=20923960]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923960; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923960']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "5afc0fb53ba036cec066617a86cf551a" } } $('.js-work-strip[data-work-id=20923960]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923960,"title":"Quasi-multipliers of Hilbert and Banach C*-bimodules","internal_url":"https://www.academia.edu/20923960/Quasi_multipliers_of_Hilbert_and_Banach_C_bimodules","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630572,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630572/thumbnails/1.jpg","file_name":"1002.3886.pdf","download_url":"https://www.academia.edu/attachments/41630572/download_file","bulk_download_file_name":"Quasi_multipliers_of_Hilbert_and_Banach.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630572/1002.3886-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DQuasi_multipliers_of_Hilbert_and_Banach.pdf\u0026Expires=1740059534\u0026Signature=eDmVDGtvoewlOtY3w03BFfARJS2fVF87lNEvTWif1cbSDxXE-fkdc1Zs~-OcAcnrIcubAEwNIBNB~sJxeNNpwqte1QXMXc3mLgpZAsjKo0shNKBF-pPjqdV7sN49yx02g3~KmkNup22JAsK7kJlGadBvlIWrsJpSkNHJrph7~mWTM-nSr4x3thq-1JkIxdL6fj3WqNsobLORcoQ5ZryO6PRkxdc2vW0uPWTuV7JzIBWx48VyHIUMJWeW2oL1xFNwJTWowrsNtqJvuw455GfWh4oOyis-vprt8pnXM3YL969~irHkGmuA3VkWpR82oM5XGvnj6Qpk-BKgp-uyxieTTg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":41630571,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630571/thumbnails/1.jpg","file_name":"1002.3886.pdf","download_url":"https://www.academia.edu/attachments/41630571/download_file","bulk_download_file_name":"Quasi_multipliers_of_Hilbert_and_Banach.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630571/1002.3886-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DQuasi_multipliers_of_Hilbert_and_Banach.pdf\u0026Expires=1740059534\u0026Signature=fXETH0w1rPPBYjfz~SHg5S4ZHXeRkj20suFjc~YYZgPfQLwPxhOP6WvEYKQaogcapXyLO5avyqerjrVJlNaDCGXS82xLRDWXUIkyaogTqKQZ0URjrYiBonuWDf-QSluNjZtBzWLL2HKyohZ4X-1te7RN~yfvC9k3HSVM29MQzNhiSGmJyPHJVS7mUxQrYR9EyFre~4ItqpYTcs0JZxEgAyVFShlB8X6fecculBb7A47xpZ6VbBOJXwsKtfsKqiJlVF--Trv44O2TgtMbl9W~VLHDT7XjfKlghzWC2jKv8SXaHhD0rwMiNvvXfRzmksOSepDe5Eb92mkmkwpxG1mJgA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923959"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923959/Completions_of_countable_non_standard_models_of_Q"><img alt="Research paper thumbnail of Completions of countable non-standard models of Q" class="work-thumbnail" src="https://attachments.academia-assets.com/41630679/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923959/Completions_of_countable_non_standard_models_of_Q">Completions of countable non-standard models of Q</a></div><div class="wp-workCard_item"><span>Eprint Arxiv Math 0604466</span><span>, Apr 21, 2006</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this note, we study non-standard models of the rational numbers with countably many elements. ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this note, we study non-standard models of the rational numbers with countably many elements. These are ordered fields, and so it makes sense to complete them, using non-standard Cauchy sequences. The main result of this note shows that these completions are real closed, i.e. each positive number is a square, and each polynomial of odd degree has a root. This way, we give a direct proof of a consequence of a theorem of Hauschild. In a previous version of this note, not being aware of these results, we missed to mention this reference. We thank Matthias Aschenbrenner for pointing out this and related work. We also give some information about the set of real parts of the finite elements of such completions -about the more interesting results along this we have been informed by Matthias Aschenbrenner. The main idea to achieve the results relies on a way to describe real zeros of a polynomial in terms of first order logic. This is achieved by carefully using the sign changes of such a polynomial.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="cbd4f20d33d1a4b405d50e22c02595ff" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630679,"asset_id":20923959,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630679/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923959"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923959"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923959; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923959]").text(description); $(".js-view-count[data-work-id=20923959]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923959; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923959']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "cbd4f20d33d1a4b405d50e22c02595ff" } } $('.js-work-strip[data-work-id=20923959]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923959,"title":"Completions of countable non-standard models of Q","internal_url":"https://www.academia.edu/20923959/Completions_of_countable_non_standard_models_of_Q","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630679,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630679/thumbnails/1.jpg","file_name":"Completions_of_countable_non-standard_mo20160127-7394-1d0758t.pdf","download_url":"https://www.academia.edu/attachments/41630679/download_file","bulk_download_file_name":"Completions_of_countable_non_standard_mo.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630679/Completions_of_countable_non-standard_mo20160127-7394-1d0758t-libre.pdf?1453898567=\u0026response-content-disposition=attachment%3B+filename%3DCompletions_of_countable_non_standard_mo.pdf\u0026Expires=1740059534\u0026Signature=NHNYCqZKjOW~hr4Ulo0XQbQxEMBBbQYX46UbknxGfCqd9ybUEnhCJmGfW1w7Ok6CrDB9~kpYvY6aj6MpcwkC1VwEc98AGliD8cQIh9R6JXNpZkWtGMp8Tlo~PAWTYgulhJkPKFnyaEB5OIZV8b1Ic01j90HJn9F3uyLlx77LRKes22c7yzNEQy3G1PzZ3QiwHAEOzN-vbEmQEkPHZ-LEbMTki5Dbdwb2uhRSxXyDokbxG2KrBSSzhVjj2ZutsqmiUqkv-HG8lB-qN9AjJ1JibwZme4nzCjcTB0Qf8-RTHuj8~5CjVLvbSanHdp5x5b4JGsb~1IoeTqLKIhkGq9w4bg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923958"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923958/Loop_groups_and_string_topology"><img alt="Research paper thumbnail of Loop groups and string topology" class="work-thumbnail" src="https://attachments.academia-assets.com/41630568/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923958/Loop_groups_and_string_topology">Loop groups and string topology</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Survey article on loop groups and their representations, following a course of three lectures hel...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Survey article on loop groups and their representations, following a course of three lectures held at the summer school "algebraic groups" at the Georg-August-Universitaet zu Goettingen, June 27--July 13, 2005. We discuss loop groups, their central extensions, and positive energy representations.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="07d67592c06f4a468a0022ef2e01c829" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630568,"asset_id":20923958,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630568/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923958"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923958"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923958; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923958]").text(description); $(".js-view-count[data-work-id=20923958]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923958; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923958']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "07d67592c06f4a468a0022ef2e01c829" } } $('.js-work-strip[data-work-id=20923958]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923958,"title":"Loop groups and string topology","internal_url":"https://www.academia.edu/20923958/Loop_groups_and_string_topology","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630568,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630568/thumbnails/1.jpg","file_name":"0802.3719.pdf","download_url":"https://www.academia.edu/attachments/41630568/download_file","bulk_download_file_name":"Loop_groups_and_string_topology.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630568/0802.3719-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DLoop_groups_and_string_topology.pdf\u0026Expires=1740059534\u0026Signature=FOhqc6jb2HZUHHtlajR6FChfGtJMVbFHCHMNMpdbkcf0iZ2GtutVOxRIkkqIXtyJ46CxdPSxIaeJPDwk5HeqcMp6sJqlqj05PTfhvgZTbD5FmpY7VUpOrH2elbtMQJkR3YkwzBqQP8Yx70HPqI7-Czh4WB5whKNcSZmHTFztf5b85ktJoqLiVIoAkdAojpucZn-wryPh8HttGxuDJ2ONLw5DP2HSy5PvQquSbrDLGWfj-UYoTpuowCfSUEA~GXGxDe6CIhnGlp2gc0wGcsd946euqED6vNBJp1K2zqOdw8gVH7f-wh4jUPBXEzPatnHCd0osQT~hJN5TcCKvtgdp-g__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":41630567,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630567/thumbnails/1.jpg","file_name":"0802.3719.pdf","download_url":"https://www.academia.edu/attachments/41630567/download_file","bulk_download_file_name":"Loop_groups_and_string_topology.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630567/0802.3719-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DLoop_groups_and_string_topology.pdf\u0026Expires=1740059534\u0026Signature=et-fo83~hLfWFEKHxv35qqdkCxVkzacECXTzOJi1LPzX99wBBRjBtprp7NKsTlIg10Cr5cD9YKGZmqCyv9gxMX4XwiuG2a2aBp3-eEPbgYN5jMflkxUwIkDSORhPCqvF7XtB0JOKiMKY-4D~PTR4LW~093D5P6z7eQBqG1FeaD8l67KwSdXDVsryXnPk9SQiRNbo45nrqQrFWpWLzp~xgo79DOFlONu2whgj40SZzmVHqYfyIB5rLVMw3W-tP0E3NX-dciveLpPmM1HoiZVHm10O~k-JLTXHAuInHEFiQlpJx~R9uaQhl-0madcW-cdQ358HLajOZBX8GWz~3PWzvg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923957"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923957/A_K_theoretic_proof_of_Boutet_de_Monvels_index_theorem_for_boundary_value_problems"><img alt="Research paper thumbnail of A K -theoretic proof of Boutet de Monvel's index theorem for boundary value problems" class="work-thumbnail" src="https://attachments.academia-assets.com/41630565/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923957/A_K_theoretic_proof_of_Boutet_de_Monvels_index_theorem_for_boundary_value_problems">A K -theoretic proof of Boutet de Monvel's index theorem for boundary value problems</a></div><div class="wp-workCard_item"><span>J Reine Angew Math</span><span>, 2006</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">0->K_i(C(X))->K_i(A/K)->K_{1-i}(C_0(T*X'))->0, i= 0,1, which split, where K denotes the compact i...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">0->K_i(C(X))->K_i(A/K)->K_{1-i}(C_0(T*X'))->0, i= 0,1, which split, where K denotes the compact ideal and T*X' the cotangent bundle of the interior of X. Using only simple K-theoretic arguments and the Atiyah-Singer Index Theorem, we show that the Fredholm index of an elliptic element in A is given as the composition of the topological index with mapping K_1(A/K)->K_0(C_0(T*X')) defined above. This relation was first established by Boutet de Monvel by different methods.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7d529bc53f4bd14d781423c6c37d1d84" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630565,"asset_id":20923957,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630565/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923957"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923957"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923957; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923957]").text(description); $(".js-view-count[data-work-id=20923957]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923957; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923957']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "7d529bc53f4bd14d781423c6c37d1d84" } } $('.js-work-strip[data-work-id=20923957]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923957,"title":"A K -theoretic proof of Boutet de Monvel's index theorem for boundary value problems","internal_url":"https://www.academia.edu/20923957/A_K_theoretic_proof_of_Boutet_de_Monvels_index_theorem_for_boundary_value_problems","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630565,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630565/thumbnails/1.jpg","file_name":"0403059.pdf","download_url":"https://www.academia.edu/attachments/41630565/download_file","bulk_download_file_name":"A_K_theoretic_proof_of_Boutet_de_Monvels.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630565/0403059-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DA_K_theoretic_proof_of_Boutet_de_Monvels.pdf\u0026Expires=1740059534\u0026Signature=C5AQzGzw8ZwsTFv1k~Ox18gSEsC1a1b0WebBScK9HDs9phmRn7NibNvZIYWo~oJGKpG1WvmHeOfO55Tz8yuKfsX84nlxz7P73Z0rTnz22I~aEO3ENAQiJj-RhPcRvngA4xWJsSu02VzErY64IvB33VGTCkPs1dfKroKvP~HA~VzLdrTLV74eFSc8fzeZXWMCj1gwAfir7CXb-QdUVvKSuj~yWau6uLUu-IgG923iNfg7TEKkGjgHIII1VcoPofRrPsrEANt~SnaxIg~DExN6HoSD4lRulFA-eK4TNbr2v1eoNmHvFAY8Pedvx6FaeQDht9Pn1oqfiJryFD3aOUqabQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":41630566,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630566/thumbnails/1.jpg","file_name":"0403059.pdf","download_url":"https://www.academia.edu/attachments/41630566/download_file","bulk_download_file_name":"A_K_theoretic_proof_of_Boutet_de_Monvels.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630566/0403059-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DA_K_theoretic_proof_of_Boutet_de_Monvels.pdf\u0026Expires=1740059534\u0026Signature=RsOfr2zv5bZPOpGABRt2kTBVSHQs52cRW1sPsR14-ristSJQaIohhhUsfuCCRm0LkzzxKkFAWunK10gsMOMEMgfonM5qcSWTLivsvDYXWbEuXGdCFa5CsK8OtzBCar7RdC5SK8A94NkFno8TsveHS-Y6cAzO~~yBsdmPwR5~Ty1ONPtHom5ddPCV0yjqmA5Api-81254pdPLTB-WHx-EueD9UF4eOW3B3JRHQJsufI2vjtizZW0IvCTFsHOgj85LIr9EagXjFPta3V1hMoojqNLaqhJfEjEU2KUZlOLI5riXSyf-qv8~FHyO8j8ETmLJKYWzb4TP3S0GvvlKIZMt8w__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923956"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923956/Real_versus_complex_K_theory_using_Kasparovs_bivariant_KK_theory"><img alt="Research paper thumbnail of Real versus complex K�theory using Kasparov's bivariant KK�theory" class="work-thumbnail" src="https://attachments.academia-assets.com/41630561/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923956/Real_versus_complex_K_theory_using_Kasparovs_bivariant_KK_theory">Real versus complex K�theory using Kasparov's bivariant KK�theory</a></div><div class="wp-workCard_item"><span>Algebr Geom Topol</span><span>, 2004</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-th...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C^*-algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the Baum-Connes conjecture for a discrete group to its complex counterpart. In particular, the complex Baum-Connes assembly map is an isomorphism if and only if the real one is, thus reproving a result of Baum and Karoubi. After inverting 2, the same is true for the injectivity or surjectivity part alone.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1c2d40c766bd65234667f3fb79921340" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630561,"asset_id":20923956,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630561/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923956"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923956"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923956; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923956]").text(description); $(".js-view-count[data-work-id=20923956]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923956; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923956']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "1c2d40c766bd65234667f3fb79921340" } } $('.js-work-strip[data-work-id=20923956]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923956,"title":"Real versus complex K�theory using Kasparov's bivariant KK�theory","internal_url":"https://www.academia.edu/20923956/Real_versus_complex_K_theory_using_Kasparovs_bivariant_KK_theory","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630561,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630561/thumbnails/1.jpg","file_name":"0311295.pdf","download_url":"https://www.academia.edu/attachments/41630561/download_file","bulk_download_file_name":"Real_versus_complex_K_theory_using_Kaspa.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630561/0311295-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DReal_versus_complex_K_theory_using_Kaspa.pdf\u0026Expires=1740059534\u0026Signature=TQr7ZkNNnRou6hjB1Za0t~YloWYQ-GREdNPu7uLPJ1x43CXEYEWO3IvtKL6jZcoTr8zTovzlWc7dYTJrq7X5t3rEpJm-AOp979ys5SAOkrP4bCikwgjVqhSUybtfU~GFcji~XChKHflFDu4gVrwMCJsHC9ksWP8jJpzv6iqsEF5m7KMJJfIKF1YIrcijFWR3f0KIA5dxFnygDmLR-LNiNaDrVq46oDqum9Sj~2GqlEmZxB-Uu6gNJXac7toobKD7~SAOKSpxj9ryxaJ9az3TDl-82UHuDx-0mPGgKmH97r~1SvTVEyNZMBEORaq6azt~W7mhjHGMnL0BH00YPp9vgQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923955"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923955/Large_time_limit_and_local_L_2_index_theorems_for_families"><img alt="Research paper thumbnail of Large time limit and local L^2-index theorems for families" class="work-thumbnail" src="https://attachments.academia-assets.com/41630562/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923955/Large_time_limit_and_local_L_2_index_theorems_for_families">Large time limit and local L^2-index theorems for families</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We compute explicitly, and without any extra regularity assumptions, the large time limit of the ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We compute explicitly, and without any extra regularity assumptions, the large time limit of the fibrewise heat operator for Bismut-Lott type superconnections in the L^2-setting. This is motivated by index theory on certain non-compact spaces (families of manifolds with cocompact group action) where the convergence of the heat operator at large time implies refined L^2-index formulas. As applications, we prove a local L^2-index theorem for families of signature operators and an L^2-Bismut-Lott theorem, expressing the Becker-Gottlieb transfer of flat bundles in terms of Kamber-Tandeur classes. With slightly stronger regularity we obtain the respective refined versions: we construct L^2-eta forms and L^2-torsion forms as transgression forms.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="92b287cb8de180e42eb47c2308457ab1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630562,"asset_id":20923955,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630562/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923955"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923955"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923955; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923955]").text(description); $(".js-view-count[data-work-id=20923955]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923955; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923955']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "92b287cb8de180e42eb47c2308457ab1" } } $('.js-work-strip[data-work-id=20923955]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923955,"title":"Large time limit and local L^2-index theorems for families","internal_url":"https://www.academia.edu/20923955/Large_time_limit_and_local_L_2_index_theorems_for_families","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630562,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630562/thumbnails/1.jpg","file_name":"1306.5659.pdf","download_url":"https://www.academia.edu/attachments/41630562/download_file","bulk_download_file_name":"Large_time_limit_and_local_L_2_index_the.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630562/1306.5659-libre.pdf?1453898587=\u0026response-content-disposition=attachment%3B+filename%3DLarge_time_limit_and_local_L_2_index_the.pdf\u0026Expires=1740059534\u0026Signature=WwK~lxny6i8UQkYYIwF9hZaFmijUJq58iFjAoOsaLVdoun2x1m8Vf6EgtX9N~oMePjqcFVFxrZMCuHzKk1G5-0-fsmJY9MGg3v6IPxIqf82hrrtXWL6FMCkvlK4kDedhB36CHmcru1g2UPkB8S3CLzaA~xvqyp0w1QJqUea3PsNtpwDDxsP4n1U7VJH7miF6DTjhK6Xddr4Klx8UAcIJPHfPuRH0XhZEn-uS7MWhXEuE4E0-ebE2Raa8DPCiZpkaMaDNuJYBk8DYKIHHesHMjmf5MR8q98phHSZgUh83RdWBupKAod~lN~fTwkPJB40lTBArh9FJnrPYVTBehm9jWQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":41630563,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630563/thumbnails/1.jpg","file_name":"1306.5659.pdf","download_url":"https://www.academia.edu/attachments/41630563/download_file","bulk_download_file_name":"Large_time_limit_and_local_L_2_index_the.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630563/1306.5659-libre.pdf?1453898589=\u0026response-content-disposition=attachment%3B+filename%3DLarge_time_limit_and_local_L_2_index_the.pdf\u0026Expires=1740059534\u0026Signature=MvsilIVh5Olc08Su5asqcmvpUx7BZeGhZPF2~ywuSRgSeMCHAElQ-mdKNc5EGMvEyGKbs23lfBUsuidr35a7eKdeIFd5KC3tR8w2idyv2mWW-Kjgf~Gb74HX-hoDVTmHYRhOflWhQLg1EjRkjNcZhVf2R5eJnyu9NvOwk-1kZxA2MDLTQq62zm8EgFf~hnWUEpFinWjkfzxpLXHX8ZbzVi7wc-9aROryUW2StTJJOXwwEDBtwTlkiLeXMzTZhQN1n9LHp-1due~qCbMbwJjoRqiE-ZdjkqfjeI~cc-MlNDcXIXE1IknKngyRaWkRxauNXa35jew0ku~tQOKMfPw0sw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923954"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/20923954/Loop_groups_and_string_topology_Lectures_for_the_summer_school_algebraic_groups_Gottingen_July_2005"><img alt="Research paper thumbnail of Loop groups and string topology Lectures for the summer school algebraic groups Gottingen, July 2005" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/20923954/Loop_groups_and_string_topology_Lectures_for_the_summer_school_algebraic_groups_Gottingen_July_2005">Loop groups and string topology Lectures for the summer school algebraic groups Gottingen, July 2005</a></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923954"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923954"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923954; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923954]").text(description); $(".js-view-count[data-work-id=20923954]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923954; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923954']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=20923954]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923954,"title":"Loop groups and string topology Lectures for the summer school algebraic groups Gottingen, July 2005","internal_url":"https://www.academia.edu/20923954/Loop_groups_and_string_topology_Lectures_for_the_summer_school_algebraic_groups_Gottingen_July_2005","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923953"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923953/The_strong_Atiyah_conjecture_for_right_angled_Artin_and_Coxeter_groups"><img alt="Research paper thumbnail of The strong Atiyah conjecture for right-angled Artin and Coxeter groups" class="work-thumbnail" src="https://attachments.academia-assets.com/41630560/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923953/The_strong_Atiyah_conjecture_for_right_angled_Artin_and_Coxeter_groups">The strong Atiyah conjecture for right-angled Artin and Coxeter groups</a></div><div class="wp-workCard_item"><span>Geom Dedic</span><span>, Oct 4, 2010</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter grou...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter groups. More generally, we prove it for groups which are certain finite extensions or elementary amenable extensions of such groups.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="c7f9568073a088582f0a93d8b7367229" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630560,"asset_id":20923953,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630560/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923953"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923953"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923953; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923953]").text(description); $(".js-view-count[data-work-id=20923953]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923953; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923953']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "c7f9568073a088582f0a93d8b7367229" } } $('.js-work-strip[data-work-id=20923953]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923953,"title":"The strong Atiyah conjecture for right-angled Artin and Coxeter groups","internal_url":"https://www.academia.edu/20923953/The_strong_Atiyah_conjecture_for_right_angled_Artin_and_Coxeter_groups","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630560,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630560/thumbnails/1.jpg","file_name":"1010.0606.pdf","download_url":"https://www.academia.edu/attachments/41630560/download_file","bulk_download_file_name":"The_strong_Atiyah_conjecture_for_right_a.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630560/1010.0606-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DThe_strong_Atiyah_conjecture_for_right_a.pdf\u0026Expires=1740046991\u0026Signature=W3CATHtCpH32cG3Y0ntSrebeBUSV-4iqAV4pajRfTXFirZeFTrA5UfM4h74gPfVGw1xQDrKxohb05y6xWSKvxHu4tHPLZ00tbYxM5v2KXDj3y4vFCdkPhLg6Iur0jX~no8O5PwBRnwYjnMWuxiotQS5ETWWfmtbhoPLA-qoDyW7QgFIUeXoR0~oAqKQTYvrtU3dBNolEdIiuK6bsfEhJ8aP59MrE8wtsph2TE-HxgWBjM2gRiFJjiP9KHYX-7wGaXwgCdmfSWtWA94ONn~HZueKk760uXsxSJDYrRvAiwvztIzSzBAdFwzLGDOIeoLiXWNPxN19bkdomABKSsrM7XA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923952"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923952/Buildings_have_finite_asymptotic_dimension"><img alt="Research paper thumbnail of Buildings have finite asymptotic dimension" class="work-thumbnail" src="https://attachments.academia-assets.com/41630675/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923952/Buildings_have_finite_asymptotic_dimension">Buildings have finite asymptotic dimension</a></div><div class="wp-workCard_item"><span>Russian Journal of Mathematical Physics</span><span>, Sep 12, 2009</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">It is proved that the asymptotic dimension of any building is finite and equal to the asymptotic ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">It is proved that the asymptotic dimension of any building is finite and equal to the asymptotic dimension of an apartment in that building.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="03981a3d5edf18c89f48bf2ebb465b5d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630675,"asset_id":20923952,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630675/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923952"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923952"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923952; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923952]").text(description); $(".js-view-count[data-work-id=20923952]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923952; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923952']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "03981a3d5edf18c89f48bf2ebb465b5d" } } $('.js-work-strip[data-work-id=20923952]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923952,"title":"Buildings have finite asymptotic dimension","internal_url":"https://www.academia.edu/20923952/Buildings_have_finite_asymptotic_dimension","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630675,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630675/thumbnails/1.jpg","file_name":"Buildings_have_finite_asymptotic_dimensi20160127-21972-102nptw.pdf","download_url":"https://www.academia.edu/attachments/41630675/download_file","bulk_download_file_name":"Buildings_have_finite_asymptotic_dimensi.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630675/Buildings_have_finite_asymptotic_dimensi20160127-21972-102nptw-libre.pdf?1453898568=\u0026response-content-disposition=attachment%3B+filename%3DBuildings_have_finite_asymptotic_dimensi.pdf\u0026Expires=1740046991\u0026Signature=LQ7uNpV6F2ZrFmaa7blONiV7jm9b3VPGSD1zkb300T7aIaeMPLgYKpOoCFqQVZ5qMI-gL2-BfDTDZ60m712XMZ3932VODWb1F~MZtUQHhKad9JtiAtibDDi5XskmkAOxhf7dNK2N8kXwdH-NPeVTGcqNhS72UN4xi26hCDM1GN45B3~DcHPixvUhdMcsJGkkpkLngzhhNpPM1oYnipbO16CDktaEm1hyUblv3OYL~9w~4OrNQuueVXvURVW6GlL4B6PqrW6ckjBx7-rfkM~txhuaZLRBbcxQlXk~IGFM4DgoDAJeTIV~fTa7oEWX4jl8dH6qr~xd7c9GK-BNL06gEg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923951"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923951/Bordism_rho_invariants_and_the_Baum_Connes_conjecture"><img alt="Research paper thumbnail of Bordism, rho-invariants and the Baum-Connes conjecture" class="work-thumbnail" src="https://attachments.academia-assets.com/41630668/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923951/Bordism_rho_invariants_and_the_Baum_Connes_conjecture">Bordism, rho-invariants and the Baum-Connes conjecture</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let G be a finitely generated discrete group. In this paper we establish vanishing results for rh...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let G be a finitely generated discrete group. In this paper we establish vanishing results for rho-invariants associated to (i) the spin-Dirac operator of a spin manifold with positive scalar curvature (ii) the signature operator of the disjoint union of a pair of homotopy equivalent oriented manifolds with fundamental group G. The invariants we consider are more precisely - the Atiyah-Patodi-Singer rho-invariant associated to a pair of finite dimensional unitary representations. - the L2-rho invariant of Cheeger-Gromov - the delocalized eta invariant of Lott for a finite conjugacy class of G. We prove that all these rho-invariants vanish if the group G is torsion-free and the Baum-Connes map for the maximal group C^*-algebra is bijective. For the delocalized invariant we only assume the validity of the Baum-Connes conjecture for the reduced C^*-algebra. In particular, the three rho-invariants associated to the signature operator are, for such groups, homotopy invariant. For the APS and the Cheeger-Gromov rho-invariants the latter result had been established by Navin Keswani. Our proof re-establishes this result and also extends it to the delocalized eta-invariant of Lott. Our method also gives some information about the eta-invariant itself (a much more saddle object than the rho-invariant).</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7a83ce4a538f13f8e9b945f334dd37dd" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630668,"asset_id":20923951,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630668/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923951"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923951"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923951; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923951]").text(description); $(".js-view-count[data-work-id=20923951]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923951; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923951']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "7a83ce4a538f13f8e9b945f334dd37dd" } } $('.js-work-strip[data-work-id=20923951]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923951,"title":"Bordism, rho-invariants and the Baum-Connes conjecture","internal_url":"https://www.academia.edu/20923951/Bordism_rho_invariants_and_the_Baum_Connes_conjecture","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630668,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630668/thumbnails/1.jpg","file_name":"Bordism_rho_invariants_and_the_Baum-Connes_conjecture_final_published_ante_proofreading.pdf","download_url":"https://www.academia.edu/attachments/41630668/download_file","bulk_download_file_name":"Bordism_rho_invariants_and_the_Baum_Conn.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630668/Bordism_rho_invariants_and_the_Baum-Connes_conjecture_final_published_ante_proofreading-libre.pdf?1453898587=\u0026response-content-disposition=attachment%3B+filename%3DBordism_rho_invariants_and_the_Baum_Conn.pdf\u0026Expires=1740059534\u0026Signature=ETOhBpK4kDoJad4WLFmh0Tk4ZuIhksQ0Ry9mO0a47ubbHSR82jGDZ36rwl3gjGki30EMvnJQDLky09dC~IyzFxY-KpJJQtsQd4MUBcYc5N5AQ1WjfqZuZyupQVwa625v1kDPmVhlh2KjyZOgl4KaBW34BrZ8ELKRu1~pzfp6rKggVizsZ0O~K31Ve9uY2H9ZJUPIAkTVk5nO2W2NeYtWkB2b2rBksC5kPFP391wJqvEoxOBj8VQyd~HK9tUP9YBKC6WVkq0NyOlkGOZZggaZt0e57ZsvRyZ51haRJYJUj-UkGqXWploXSZyK68qItB7pJ2YYZHZVnPxuvce4wh5AgA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923950"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923950/Duality_for_topological_abelian_group_stacks_and_T_duality"><img alt="Research paper thumbnail of Duality for topological abelian group stacks and T-duality" class="work-thumbnail" src="https://attachments.academia-assets.com/41630558/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923950/Duality_for_topological_abelian_group_stacks_and_T_duality">Duality for topological abelian group stacks and T-duality</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">v2: An additional assumption was added in Theorem 4.8. In order to show that a connected abelian ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">v2: An additional assumption was added in Theorem 4.8. In order to show that a connected abelian group is admissible on the site of locally compact spaces we must in addition assume that it is locally topologically divisible. This condition is used in the proof of Lemma 4.62.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="dfb111dcea0f4822c71efc54a098dae1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630558,"asset_id":20923950,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630558/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923950"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923950"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923950; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923950]").text(description); $(".js-view-count[data-work-id=20923950]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923950; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923950']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "dfb111dcea0f4822c71efc54a098dae1" } } $('.js-work-strip[data-work-id=20923950]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923950,"title":"Duality for topological abelian group stacks and T-duality","internal_url":"https://www.academia.edu/20923950/Duality_for_topological_abelian_group_stacks_and_T_duality","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630558,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630558/thumbnails/1.jpg","file_name":"0701428.pdf","download_url":"https://www.academia.edu/attachments/41630558/download_file","bulk_download_file_name":"Duality_for_topological_abelian_group_st.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630558/0701428-libre.pdf?1453898597=\u0026response-content-disposition=attachment%3B+filename%3DDuality_for_topological_abelian_group_st.pdf\u0026Expires=1740059534\u0026Signature=TavBJM8fH7PuD6rZt9HX5seVF0wOWjWSGJEhFr~UoC6vUky8UJftFIu6AqWno9mZErShwnO0L~bdc9qvd9k8CXMgcoauXbOltuTgzjoh4mr17cnVtnuvXVKGU7wBamjDbcA3ife1S4zpPl8YvjeVqlhQLhXIg0jayPymPHe5fRidkGjElU7Aq3MAdcCmow1UHLJg6lp2hDInNOc~tJJnUzo3JO1HO67tVmWTpRa-fwpRqx6j8B0Dn1i~t2tIDx2KSlKp3dQzCjENdrwH9tVPf45B6GDvniCzTyPUPoS9smNlfUsxycxw0COYH172JIIYu9ZnDSd6uYi3N8bzqdUmYA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":41630557,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630557/thumbnails/1.jpg","file_name":"0701428.pdf","download_url":"https://www.academia.edu/attachments/41630557/download_file","bulk_download_file_name":"Duality_for_topological_abelian_group_st.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630557/0701428-libre.pdf?1453898597=\u0026response-content-disposition=attachment%3B+filename%3DDuality_for_topological_abelian_group_st.pdf\u0026Expires=1740059534\u0026Signature=bYqJx8h07gG1sgEbJKMg6vAsUMMXKbsaNw2I1y4a-ewUw5AoRhjEBfCbpz8rlJmoMqWMx-sY181ooH-ailzyhqJdtMVNM1fS0IA22KVGoFPD8CDrnbYTW6SeK~njppWn7zXvgLJ4oCu0MV8OFGrdrDb0KCEknuVoise-8KO9S1ySsHWhQ387UhMj-JvxU2yrhvfhtICytaGWT0-aL8MD2lh3MCSae~bNVrECjQGj4edyjN2PG7w0LZCm-~aEXxCfsiukppRXeS5MgkkiaALmY8k3-60uQMee2-6PS~9n7-czTOjnIYU8xa7pWTsJszVVDiagnPyXym375nqsOVOL2A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923949"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923949/Various_L_2_signatures_and_a_topological_L_2_signature_theorem"><img alt="Research paper thumbnail of Various L 2 -signatures and a topological L 2 -signature theorem" class="work-thumbnail" src="https://attachments.academia-assets.com/41630670/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923949/Various_L_2_signatures_and_a_topological_L_2_signature_theorem">Various L 2 -signatures and a topological L 2 -signature theorem</a></div><div class="wp-workCard_item"><span>High-Dimensional Manifold Topology</span><span>, 2003</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">For a normal covering over a closed oriented topological manifold we give a proof of the L 2 -sig...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">For a normal covering over a closed oriented topological manifold we give a proof of the L 2 -signature theorem with twisted coefficients, using Lipschitz structures and the Lipschitz signature operator introduced by Teleman. We also prove that the L-theory isomorphism conjecture as well as the C * max -version of the Baum-Connes conjecture imply the L 2signature theorem for a normal covering over a Poincaré space, provided that the group of deck transformations is torsion-free.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="74880b3084550204238edee0f9fefe46" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630670,"asset_id":20923949,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630670/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923949"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923949"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923949; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923949]").text(description); $(".js-view-count[data-work-id=20923949]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923949; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923949']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "74880b3084550204238edee0f9fefe46" } } $('.js-work-strip[data-work-id=20923949]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923949,"title":"Various L 2 -signatures and a topological L 2 -signature theorem","internal_url":"https://www.academia.edu/20923949/Various_L_2_signatures_and_a_topological_L_2_signature_theorem","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630670,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630670/thumbnails/1.jpg","file_name":"Various_L2-signatures_and_a_topological_20160127-16054-1xnvt88.pdf","download_url":"https://www.academia.edu/attachments/41630670/download_file","bulk_download_file_name":"Various_L_2_signatures_and_a_topological.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630670/Various_L2-signatures_and_a_topological_20160127-16054-1xnvt88-libre.pdf?1453898571=\u0026response-content-disposition=attachment%3B+filename%3DVarious_L_2_signatures_and_a_topological.pdf\u0026Expires=1740059534\u0026Signature=G7XQKYRW77omN3FtWEkCWpzrX7Jy54NeLVaJtHBzPg3-pjzadLfeQv15Bdk~ikUaB6CafceaOczNEZ3CfIKvlOgm-5xBsuv-CWrQNvx09kPnpuxc5bvUzy3d24QopelnGwRCH3aCl5ed3Duss1k8S8aRUVMkE-uGKz4WBgdYE3OQRM5HuNnv39buM6N4QrhJ0kp52ikn3GTfvqyNM-jyZ4ax2bPFg0nz681UDhy5ryVTlkGfWx8K1tzqXXok~zYDq9yvo-8xsu3D4YM5sUsmlbUF6z94SLHClQj-MZKVR9DwHh7uiBDIxIyy4NGEGMyryzO8f3Bo83IR0nyDTxVi2Q__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="3677049" id="papers"><div class="js-work-strip profile--work_container" data-work-id="20923975"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/20923975/Analysis_on_manifolds_of_bounded_geometry_Hodge_De_Rham_isomorphism_and_L_2_index_theorem"><img alt="Research paper thumbnail of Analysis on ∂-manifolds of bounded geometry, Hodge-De Rham isomorphism and L[2]-index theorem" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/20923975/Analysis_on_manifolds_of_bounded_geometry_Hodge_De_Rham_isomorphism_and_L_2_index_theorem">Analysis on ∂-manifolds of bounded geometry, Hodge-De Rham isomorphism and L[2]-index theorem</a></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923975"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923975"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923975; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923975]").text(description); $(".js-view-count[data-work-id=20923975]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923975; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923975']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=20923975]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923975,"title":"Analysis on ∂-manifolds of bounded geometry, Hodge-De Rham isomorphism and L[2]-index theorem","internal_url":"https://www.academia.edu/20923975/Analysis_on_manifolds_of_bounded_geometry_Hodge_De_Rham_isomorphism_and_L_2_index_theorem","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923973"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/20923973/Modern_index_Theory_lectures_held_at_CIRM_rencontre_Theorie_dindice_Mar_2006"><img alt="Research paper thumbnail of Modern index Theory — lectures held at CIRM rencontre "Theorie d'indice", Mar 2006" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/20923973/Modern_index_Theory_lectures_held_at_CIRM_rencontre_Theorie_dindice_Mar_2006">Modern index Theory — lectures held at CIRM rencontre "Theorie d'indice", Mar 2006</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923973"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923973"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923973; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923973]").text(description); $(".js-view-count[data-work-id=20923973]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923973; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923973']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=20923973]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923973,"title":"Modern index Theory — lectures held at CIRM rencontre \"Theorie d'indice\", Mar 2006","internal_url":"https://www.academia.edu/20923973/Modern_index_Theory_lectures_held_at_CIRM_rencontre_Theorie_dindice_Mar_2006","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923967"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923967/A_counterexample_to_a_conjecture_about_positive_scalar_curvature"><img alt="Research paper thumbnail of A counterexample to a conjecture about positive scalar curvature" class="work-thumbnail" src="https://attachments.academia-assets.com/41630683/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923967/A_counterexample_to_a_conjecture_about_positive_scalar_curvature">A counterexample to a conjecture about positive scalar curvature</a></div><div class="wp-workCard_item"><span>Proceedings of the American Mathematical Society</span><span>, 2015</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">1, Conjecture 1] asserts that a closed smooth manifold M with non-spin universal covering admits ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">1, Conjecture 1] asserts that a closed smooth manifold M with non-spin universal covering admits a metric of positive scalar curvature if and only if a certain homological condition is satisfied. We present a counterexample to this conjecture, based on the counterexample to the unstable Gromov-Lawson-Rosenberg conjecture given in .</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="3bd0b7f09816e4417c01bf40cd197abe" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630683,"asset_id":20923967,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630683/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923967"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923967"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923967; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923967]").text(description); $(".js-view-count[data-work-id=20923967]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923967; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923967']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "3bd0b7f09816e4417c01bf40cd197abe" } } $('.js-work-strip[data-work-id=20923967]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923967,"title":"A counterexample to a conjecture about positive scalar curvature","internal_url":"https://www.academia.edu/20923967/A_counterexample_to_a_conjecture_about_positive_scalar_curvature","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630683,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630683/thumbnails/1.jpg","file_name":"A_Counterexample_to_a_Conjecture_about_P20160127-10948-3yfu5g.pdf","download_url":"https://www.academia.edu/attachments/41630683/download_file","bulk_download_file_name":"A_counterexample_to_a_conjecture_about_p.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630683/A_Counterexample_to_a_Conjecture_about_P20160127-10948-3yfu5g-libre.pdf?1453898566=\u0026response-content-disposition=attachment%3B+filename%3DA_counterexample_to_a_conjecture_about_p.pdf\u0026Expires=1740059534\u0026Signature=N8ZGZbqds9OecywVbLTM3pxSgaGXRgYjC6mCVhvPWhD90DsPfStviNsTaFeABjCviQFhaPNIsKDxHdPkKhj6VOhDmCXL8sWSsfTen2sa6bOcrX3XJCSDNwheMqztQ1FFw27h8Q2~6-DMycm0bwaVGlk97Efi2AEwE1qT6UleTPJU7fQnGAQ-gz1v38QIOJ~Ixo1~8oM-49PszgNInDvU9Z1NjlIkT8STc4NKiN2GET3iKg2hptCHbUCaqkYaGi9VlXewNnAP1b4NsrH9gi3xe~~alfj8CRWdhLq25AQAacu-YR~Ws9xPqJP5~34CFHICm0lK2K3oP1MLBNieC9AZzw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923966"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923966/Codimension_two_index_obstructions_to_positive_scalar_curvature"><img alt="Research paper thumbnail of Codimension two index obstructions to positive scalar curvature" class="work-thumbnail" src="https://attachments.academia-assets.com/41630686/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923966/Codimension_two_index_obstructions_to_positive_scalar_curvature">Codimension two index obstructions to positive scalar curvature</a></div><div class="wp-workCard_item"><span>Annales de l’institut Fourier</span><span>, 2015</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The main result of this paper is a gneral obstruction to the existence of a metric of positive sc...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The main result of this paper is a gneral obstruction to the existence of a metric of positive scalar curvature on a compact spin manifold, given by hypersurfaces of codimension 2. The proof is based on the applicatoin of coarse indes theory to Dirac operatrs twisted by Hilbert C * -module bundles.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="701c89ff7b51464a79dd5e15d4308659" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630686,"asset_id":20923966,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630686/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923966"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923966"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923966; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923966]").text(description); $(".js-view-count[data-work-id=20923966]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923966; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923966']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "701c89ff7b51464a79dd5e15d4308659" } } $('.js-work-strip[data-work-id=20923966]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923966,"title":"Codimension two index obstructions to positive scalar curvature","internal_url":"https://www.academia.edu/20923966/Codimension_two_index_obstructions_to_positive_scalar_curvature","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630686,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630686/thumbnails/1.jpg","file_name":"Codimension_two_index_obstructions_to_po20160127-20216-1dhxq3d.pdf","download_url":"https://www.academia.edu/attachments/41630686/download_file","bulk_download_file_name":"Codimension_two_index_obstructions_to_po.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630686/Codimension_two_index_obstructions_to_po20160127-20216-1dhxq3d-libre.pdf?1453898574=\u0026response-content-disposition=attachment%3B+filename%3DCodimension_two_index_obstructions_to_po.pdf\u0026Expires=1740059534\u0026Signature=QP5rIlnZ00Ee~B6JQk3dYNjZ1yK9seQtaoiql0GRxUQEP4tUgCUjX6hjfQwb1-YgJyWEBvIu74a1evs9-W3PAvD8jIkJVbe0LoYAENT7CRZrtZc2G7QmICxGy64E1a-yBsw5mEDyd4y3mHwJI0xN3k1YRB85-Nu2zqPGNpYM2ZgLVILCETKnbNflg~GPE5mQMJHG-Xo36J~nsuBCoMgF2Nx6yt92HbPYd4rNIvx9HYD3-y3wxrFPpmxhn8ZJGexMek9q~qUhnrEPyeCWCXTHMwbM2zDO4dHv9ecg670E4aglwHW0Ji5hyfFWWGel2NzcA91Gr1d9L91cyYOyB2E4Fw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923965"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923965/The_surgery_exact_sequence_K_theory_and_the_signature_operator"><img alt="Research paper thumbnail of The surgery exact sequence, K-theory and the signature operator" class="work-thumbnail" src="https://attachments.academia-assets.com/41630690/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923965/The_surgery_exact_sequence_K_theory_and_the_signature_operator">The surgery exact sequence, K-theory and the signature operator</a></div><div class="wp-workCard_item"><span>Annals of K-Theory</span><span>, 2016</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper, we study the space of metrics of positive scalar curvature using methods from coar...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper, we study the space of metrics of positive scalar curvature using methods from coarse geometry.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="c39bba77aca27dd494a7672f4dafbe95" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630690,"asset_id":20923965,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630690/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923965"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923965"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923965; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923965]").text(description); $(".js-view-count[data-work-id=20923965]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923965; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923965']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "c39bba77aca27dd494a7672f4dafbe95" } } $('.js-work-strip[data-work-id=20923965]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923965,"title":"The surgery exact sequence, K-theory and the signature operator","internal_url":"https://www.academia.edu/20923965/The_surgery_exact_sequence_K_theory_and_the_signature_operator","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630690,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630690/thumbnails/1.jpg","file_name":"The_surgery_exact_sequence_K-theory_and_20160127-16059-mbickj.pdf","download_url":"https://www.academia.edu/attachments/41630690/download_file","bulk_download_file_name":"The_surgery_exact_sequence_K_theory_and.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630690/The_surgery_exact_sequence_K-theory_and_20160127-16059-mbickj-libre.pdf?1453898578=\u0026response-content-disposition=attachment%3B+filename%3DThe_surgery_exact_sequence_K_theory_and.pdf\u0026Expires=1740046991\u0026Signature=U9sfUYTaqLipjE4qAB5dJCmDuXwnequwJ9fPD2VgklLQ7RZScNmkMmxQN2yfS-5eGRJE8~ZSz17mw6Vd9GMMNc8OD9Bzjdcs5ou7pNOl9jNb3VmNPNhY-6455JJigMqcEtYAANuxsTp7gEXLz0mqZLCHZXEpslhZIALzPgP-oDaDRyhr7OdDq7avZZy72Jqr4bEnNCde0nml94aS4-hJOysQcN98-CgX8h4k1IvrywtnKNgZ1fu8B3BgcrJ0BhRbwTZ9f1Ph8mqM2NpuILACYoKEzkTPa9mCYK~2HMK8npAGqmuiUiMxreIbS1jg2xRVeER5tK0P7c9uLgWByes-7w__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923963"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923963/L_2_index_theorem_for_elliptic_differential_boundary_problems"><img alt="Research paper thumbnail of L 2 -index theorem for elliptic differential boundary problems" class="work-thumbnail" src="https://attachments.academia-assets.com/41630689/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923963/L_2_index_theorem_for_elliptic_differential_boundary_problems">L 2 -index theorem for elliptic differential boundary problems</a></div><div class="wp-workCard_item"><span>Pacific Journal of Mathematics</span><span>, 2001</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Suppose M is a compact manifold with boundary ∂M . Let M ↓M be a normal covering with covering gr...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Suppose M is a compact manifold with boundary ∂M . Let M ↓M be a normal covering with covering group Γ. Suppose (A, T ) is an elliptic differential boundary value problem on M with lift (Ã,T ) toM . Then the von Neumann dimension dim Γ of kernel and cokernel of this lift are defined. The main result of this paper is: these numbers are finite, and their difference, by definition the von Neumann index ind Γ (Ã,T ), equals the index of (A, T ). In this way, we extend the classical L 2 -index theorem of Atiyah to manifolds with boundary.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="573b642c81dca23d4b8e4a1874b93224" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630689,"asset_id":20923963,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630689/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923963"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923963"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923963; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923963]").text(description); $(".js-view-count[data-work-id=20923963]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923963; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923963']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "573b642c81dca23d4b8e4a1874b93224" } } $('.js-work-strip[data-work-id=20923963]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923963,"title":"L 2 -index theorem for elliptic differential boundary problems","internal_url":"https://www.academia.edu/20923963/L_2_index_theorem_for_elliptic_differential_boundary_problems","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630689,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630689/thumbnails/1.jpg","file_name":"L2-index_theorem_for_elliptic_differenti20160127-16059-9k37jf.pdf","download_url":"https://www.academia.edu/attachments/41630689/download_file","bulk_download_file_name":"L_2_index_theorem_for_elliptic_different.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630689/L2-index_theorem_for_elliptic_differenti20160127-16059-9k37jf-libre.pdf?1453898567=\u0026response-content-disposition=attachment%3B+filename%3DL_2_index_theorem_for_elliptic_different.pdf\u0026Expires=1740059534\u0026Signature=FdOKTRzSAtQN1VzECdlgp3RdcwJbjPZls3hi8XDeL9oJ1QRMqtmsZJ9zaSvWcipP3slzKWfl7u6FAO5dXrsdqHX2WPc140WSFZDECSvA1C4L6EiWtiJ7ZKjNpUgeizy5BWZwcrmMPBQ6ClCORP31mTfRsbKf3iFv2R6y0U1iM6JezJpc1TepiQ7rzHHksks01vODJYVCvVu6YGDIbaWugyTXInqSwVMXVk2zfmc3p6e-c21UuOuyMs9CQaBInSjpAl8RjIoV7wDaYa5oze4-3yV4yz8Pyad9YLfBXrLE4hou9-VHJaVlnQ7Zek~uEZwRxze5WKC3RgiORSpCFMddUw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923962"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923962/On_a_conjecture_of_Daniel_H_Gottlieb"><img alt="Research paper thumbnail of On a conjecture of Daniel H. Gottlieb" class="work-thumbnail" src="https://attachments.academia-assets.com/41630678/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923962/On_a_conjecture_of_Daniel_H_Gottlieb">On a conjecture of Daniel H. Gottlieb</a></div><div class="wp-workCard_item"><span>Eprint Arxiv Math 0702826</span><span>, Feb 1, 2007</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We give a counterexample to a conjecture of D.H. Gottlieb and prove a strengthened version of it....</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We give a counterexample to a conjecture of D.H. Gottlieb and prove a strengthened version of it. The conjecture says that a map from a finite CW-complex X to an aspherical CW-complex Y with non-zero Euler characteristic can have non-trivial degree (suitably defined) only if the centralizer of the image of the fundamental group of X is trivial. As a corollary we show that in the above situation all components of non-zero degree maps in the space of maps from X to Y are contractible.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="8f9987ececc5da7eba31813eb08b7217" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630678,"asset_id":20923962,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630678/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923962"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923962"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923962; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923962]").text(description); $(".js-view-count[data-work-id=20923962]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923962; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923962']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "8f9987ececc5da7eba31813eb08b7217" } } $('.js-work-strip[data-work-id=20923962]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923962,"title":"On a conjecture of Daniel H. Gottlieb","internal_url":"https://www.academia.edu/20923962/On_a_conjecture_of_Daniel_H_Gottlieb","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630678,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630678/thumbnails/1.jpg","file_name":"0702826.pdf","download_url":"https://www.academia.edu/attachments/41630678/download_file","bulk_download_file_name":"On_a_conjecture_of_Daniel_H_Gottlieb.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630678/0702826-libre.pdf?1453898567=\u0026response-content-disposition=attachment%3B+filename%3DOn_a_conjecture_of_Daniel_H_Gottlieb.pdf\u0026Expires=1740059534\u0026Signature=Pl7bCkxo80OP~5jlrHx0NvHZdgL3paOoVdYXD9H3vGU6cHtpVbq6NzBZEH8EIcreHEBTGw9wKHE5Kj4MKHkCxFafjbliNprpTpIYEKEIlZkqSUBRXGHO1jvSaYFjGX4ioSqXMZgd~ybQhxRKfV3yUm64taLQRVwbZV6eMBqmcyUkwkYsDPJYyEVjYe9svQI3Qopc2fl43I4-voXoeJiComz2DJnGU~imx~Er3~8Ko2T6cINwAuogNPZngrJZZIsYClaNE6Xw43Z~lbSG8q9AsJuJiddOhol-xZtNth5zqabZpNaqPtgTdKCebm9X6UK4IdSPPE5pkrsJVaddXh~z8A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923961"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923961/A_Model_for_the_Universal_Space_for_Proper_Actions_of_a_Hyperbolic_Group"><img alt="Research paper thumbnail of A Model for the Universal Space for Proper Actions of a Hyperbolic Group" class="work-thumbnail" src="https://attachments.academia-assets.com/41630681/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923961/A_Model_for_the_Universal_Space_for_Proper_Actions_of_a_Hyperbolic_Group">A Model for the Universal Space for Proper Actions of a Hyperbolic Group</a></div><div class="wp-workCard_item"><span>New York Journal of Mathematics</span><span>, Sep 13, 2002</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let $G$ be a word hyperbolic group in the sense of Gromov and $P$ its associated Rips complex. We...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let $G$ be a word hyperbolic group in the sense of Gromov and $P$ its associated Rips complex. We prove that the fixed point set $P^H$ is contractible for every finite subgroups $H$ of $G$. This is the main ingredient for proving that $P$ is a finite model for the universal space $e.g.$ of proper actions. As a corollary we get that a hyperbolic group has only finitely many conjugacy classes of finite subgroups.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="8abc73bbafefea67e09d3df6941265f3" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630681,"asset_id":20923961,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630681/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923961"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923961"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923961; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923961]").text(description); $(".js-view-count[data-work-id=20923961]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923961; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923961']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "8abc73bbafefea67e09d3df6941265f3" } } $('.js-work-strip[data-work-id=20923961]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923961,"title":"A Model for the Universal Space for Proper Actions of a Hyperbolic Group","internal_url":"https://www.academia.edu/20923961/A_Model_for_the_Universal_Space_for_Proper_Actions_of_a_Hyperbolic_Group","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630681,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630681/thumbnails/1.jpg","file_name":"A_Model_for_the_Universal_Space_for_Prop20160127-16054-1bfjnhk.pdf","download_url":"https://www.academia.edu/attachments/41630681/download_file","bulk_download_file_name":"A_Model_for_the_Universal_Space_for_Prop.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630681/A_Model_for_the_Universal_Space_for_Prop20160127-16054-1bfjnhk-libre.pdf?1453898567=\u0026response-content-disposition=attachment%3B+filename%3DA_Model_for_the_Universal_Space_for_Prop.pdf\u0026Expires=1740059534\u0026Signature=dSDQMztua8W8TkA4nLwSM9r8axtI69CPNL-ZBl7bYpJFXeKbwLbWAs7w8p8BNF2xUz6zE4kv7UqJuQlOk0doN4tBSj1XgmlkaDwsvokUlnCqtZGxI~uRNDbnTR47a-dKTXV9hWH3oYMAmUh-0DgBi4g2AiBT~1qEsffT0RL--WtIiKvMdMdo1q3JnVQkYSxdnImKOrpOQ1ubcauO~029Fk2F3I42n6fzbL8O8Mb~U7bJYH152BPCFDmZ98nuQrUXyvFMFVed7iN-gWL0DLVbM3VXNOWu~Xesamhmr6HAAqLkJ2v0JIr6WVr5fCl76QtHnncER-fSE276dNZxgPZqMQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923960"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923960/Quasi_multipliers_of_Hilbert_and_Banach_C_bimodules"><img alt="Research paper thumbnail of Quasi-multipliers of Hilbert and Banach C*-bimodules" class="work-thumbnail" src="https://attachments.academia-assets.com/41630572/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923960/Quasi_multipliers_of_Hilbert_and_Banach_C_bimodules">Quasi-multipliers of Hilbert and Banach C*-bimodules</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Quasi-multipliers for a Hilbert C*-bimodule V were introduced by Brown, Mingo and Shen 1994 as a ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Quasi-multipliers for a Hilbert C*-bimodule V were introduced by Brown, Mingo and Shen 1994 as a certain subset of the Banach bidual module V**. We give another (equivalent) definition of quasi-multipliers for Hilbert C*-bimodules using the centralizer approach and then show that quasi-multipliers are, in fact, universal (maximal) objects of a certain category. We also introduce quasi-multipliers for bimodules in Kasparov's sense and even for Banach bimodules over C*-algebras, provided these C*-algebras act non-degenerately. A topological picture of quasi-multipliers via the quasi-strict topology is given. Finally, we describe quasi-multipliers in two main situations: for the standard Hilbert bimodule l_2(A) and for bimodules of sections of Hilbert C*-bimodule bundles over locally compact spaces.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="5afc0fb53ba036cec066617a86cf551a" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630572,"asset_id":20923960,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630572/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923960"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923960"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923960; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923960]").text(description); $(".js-view-count[data-work-id=20923960]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923960; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923960']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "5afc0fb53ba036cec066617a86cf551a" } } $('.js-work-strip[data-work-id=20923960]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923960,"title":"Quasi-multipliers of Hilbert and Banach C*-bimodules","internal_url":"https://www.academia.edu/20923960/Quasi_multipliers_of_Hilbert_and_Banach_C_bimodules","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630572,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630572/thumbnails/1.jpg","file_name":"1002.3886.pdf","download_url":"https://www.academia.edu/attachments/41630572/download_file","bulk_download_file_name":"Quasi_multipliers_of_Hilbert_and_Banach.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630572/1002.3886-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DQuasi_multipliers_of_Hilbert_and_Banach.pdf\u0026Expires=1740059534\u0026Signature=eDmVDGtvoewlOtY3w03BFfARJS2fVF87lNEvTWif1cbSDxXE-fkdc1Zs~-OcAcnrIcubAEwNIBNB~sJxeNNpwqte1QXMXc3mLgpZAsjKo0shNKBF-pPjqdV7sN49yx02g3~KmkNup22JAsK7kJlGadBvlIWrsJpSkNHJrph7~mWTM-nSr4x3thq-1JkIxdL6fj3WqNsobLORcoQ5ZryO6PRkxdc2vW0uPWTuV7JzIBWx48VyHIUMJWeW2oL1xFNwJTWowrsNtqJvuw455GfWh4oOyis-vprt8pnXM3YL969~irHkGmuA3VkWpR82oM5XGvnj6Qpk-BKgp-uyxieTTg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":41630571,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630571/thumbnails/1.jpg","file_name":"1002.3886.pdf","download_url":"https://www.academia.edu/attachments/41630571/download_file","bulk_download_file_name":"Quasi_multipliers_of_Hilbert_and_Banach.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630571/1002.3886-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DQuasi_multipliers_of_Hilbert_and_Banach.pdf\u0026Expires=1740059534\u0026Signature=fXETH0w1rPPBYjfz~SHg5S4ZHXeRkj20suFjc~YYZgPfQLwPxhOP6WvEYKQaogcapXyLO5avyqerjrVJlNaDCGXS82xLRDWXUIkyaogTqKQZ0URjrYiBonuWDf-QSluNjZtBzWLL2HKyohZ4X-1te7RN~yfvC9k3HSVM29MQzNhiSGmJyPHJVS7mUxQrYR9EyFre~4ItqpYTcs0JZxEgAyVFShlB8X6fecculBb7A47xpZ6VbBOJXwsKtfsKqiJlVF--Trv44O2TgtMbl9W~VLHDT7XjfKlghzWC2jKv8SXaHhD0rwMiNvvXfRzmksOSepDe5Eb92mkmkwpxG1mJgA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923959"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923959/Completions_of_countable_non_standard_models_of_Q"><img alt="Research paper thumbnail of Completions of countable non-standard models of Q" class="work-thumbnail" src="https://attachments.academia-assets.com/41630679/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923959/Completions_of_countable_non_standard_models_of_Q">Completions of countable non-standard models of Q</a></div><div class="wp-workCard_item"><span>Eprint Arxiv Math 0604466</span><span>, Apr 21, 2006</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this note, we study non-standard models of the rational numbers with countably many elements. ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this note, we study non-standard models of the rational numbers with countably many elements. These are ordered fields, and so it makes sense to complete them, using non-standard Cauchy sequences. The main result of this note shows that these completions are real closed, i.e. each positive number is a square, and each polynomial of odd degree has a root. This way, we give a direct proof of a consequence of a theorem of Hauschild. In a previous version of this note, not being aware of these results, we missed to mention this reference. We thank Matthias Aschenbrenner for pointing out this and related work. We also give some information about the set of real parts of the finite elements of such completions -about the more interesting results along this we have been informed by Matthias Aschenbrenner. The main idea to achieve the results relies on a way to describe real zeros of a polynomial in terms of first order logic. This is achieved by carefully using the sign changes of such a polynomial.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="cbd4f20d33d1a4b405d50e22c02595ff" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630679,"asset_id":20923959,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630679/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923959"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923959"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923959; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923959]").text(description); $(".js-view-count[data-work-id=20923959]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923959; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923959']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "cbd4f20d33d1a4b405d50e22c02595ff" } } $('.js-work-strip[data-work-id=20923959]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923959,"title":"Completions of countable non-standard models of Q","internal_url":"https://www.academia.edu/20923959/Completions_of_countable_non_standard_models_of_Q","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630679,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630679/thumbnails/1.jpg","file_name":"Completions_of_countable_non-standard_mo20160127-7394-1d0758t.pdf","download_url":"https://www.academia.edu/attachments/41630679/download_file","bulk_download_file_name":"Completions_of_countable_non_standard_mo.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630679/Completions_of_countable_non-standard_mo20160127-7394-1d0758t-libre.pdf?1453898567=\u0026response-content-disposition=attachment%3B+filename%3DCompletions_of_countable_non_standard_mo.pdf\u0026Expires=1740059534\u0026Signature=NHNYCqZKjOW~hr4Ulo0XQbQxEMBBbQYX46UbknxGfCqd9ybUEnhCJmGfW1w7Ok6CrDB9~kpYvY6aj6MpcwkC1VwEc98AGliD8cQIh9R6JXNpZkWtGMp8Tlo~PAWTYgulhJkPKFnyaEB5OIZV8b1Ic01j90HJn9F3uyLlx77LRKes22c7yzNEQy3G1PzZ3QiwHAEOzN-vbEmQEkPHZ-LEbMTki5Dbdwb2uhRSxXyDokbxG2KrBSSzhVjj2ZutsqmiUqkv-HG8lB-qN9AjJ1JibwZme4nzCjcTB0Qf8-RTHuj8~5CjVLvbSanHdp5x5b4JGsb~1IoeTqLKIhkGq9w4bg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923958"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923958/Loop_groups_and_string_topology"><img alt="Research paper thumbnail of Loop groups and string topology" class="work-thumbnail" src="https://attachments.academia-assets.com/41630568/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923958/Loop_groups_and_string_topology">Loop groups and string topology</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Survey article on loop groups and their representations, following a course of three lectures hel...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Survey article on loop groups and their representations, following a course of three lectures held at the summer school "algebraic groups" at the Georg-August-Universitaet zu Goettingen, June 27--July 13, 2005. We discuss loop groups, their central extensions, and positive energy representations.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="07d67592c06f4a468a0022ef2e01c829" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630568,"asset_id":20923958,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630568/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923958"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923958"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923958; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923958]").text(description); $(".js-view-count[data-work-id=20923958]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923958; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923958']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "07d67592c06f4a468a0022ef2e01c829" } } $('.js-work-strip[data-work-id=20923958]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923958,"title":"Loop groups and string topology","internal_url":"https://www.academia.edu/20923958/Loop_groups_and_string_topology","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630568,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630568/thumbnails/1.jpg","file_name":"0802.3719.pdf","download_url":"https://www.academia.edu/attachments/41630568/download_file","bulk_download_file_name":"Loop_groups_and_string_topology.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630568/0802.3719-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DLoop_groups_and_string_topology.pdf\u0026Expires=1740059534\u0026Signature=FOhqc6jb2HZUHHtlajR6FChfGtJMVbFHCHMNMpdbkcf0iZ2GtutVOxRIkkqIXtyJ46CxdPSxIaeJPDwk5HeqcMp6sJqlqj05PTfhvgZTbD5FmpY7VUpOrH2elbtMQJkR3YkwzBqQP8Yx70HPqI7-Czh4WB5whKNcSZmHTFztf5b85ktJoqLiVIoAkdAojpucZn-wryPh8HttGxuDJ2ONLw5DP2HSy5PvQquSbrDLGWfj-UYoTpuowCfSUEA~GXGxDe6CIhnGlp2gc0wGcsd946euqED6vNBJp1K2zqOdw8gVH7f-wh4jUPBXEzPatnHCd0osQT~hJN5TcCKvtgdp-g__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":41630567,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630567/thumbnails/1.jpg","file_name":"0802.3719.pdf","download_url":"https://www.academia.edu/attachments/41630567/download_file","bulk_download_file_name":"Loop_groups_and_string_topology.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630567/0802.3719-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DLoop_groups_and_string_topology.pdf\u0026Expires=1740059534\u0026Signature=et-fo83~hLfWFEKHxv35qqdkCxVkzacECXTzOJi1LPzX99wBBRjBtprp7NKsTlIg10Cr5cD9YKGZmqCyv9gxMX4XwiuG2a2aBp3-eEPbgYN5jMflkxUwIkDSORhPCqvF7XtB0JOKiMKY-4D~PTR4LW~093D5P6z7eQBqG1FeaD8l67KwSdXDVsryXnPk9SQiRNbo45nrqQrFWpWLzp~xgo79DOFlONu2whgj40SZzmVHqYfyIB5rLVMw3W-tP0E3NX-dciveLpPmM1HoiZVHm10O~k-JLTXHAuInHEFiQlpJx~R9uaQhl-0madcW-cdQ358HLajOZBX8GWz~3PWzvg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923957"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923957/A_K_theoretic_proof_of_Boutet_de_Monvels_index_theorem_for_boundary_value_problems"><img alt="Research paper thumbnail of A K -theoretic proof of Boutet de Monvel's index theorem for boundary value problems" class="work-thumbnail" src="https://attachments.academia-assets.com/41630565/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923957/A_K_theoretic_proof_of_Boutet_de_Monvels_index_theorem_for_boundary_value_problems">A K -theoretic proof of Boutet de Monvel's index theorem for boundary value problems</a></div><div class="wp-workCard_item"><span>J Reine Angew Math</span><span>, 2006</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">0->K_i(C(X))->K_i(A/K)->K_{1-i}(C_0(T*X'))->0, i= 0,1, which split, where K denotes the compact i...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">0->K_i(C(X))->K_i(A/K)->K_{1-i}(C_0(T*X'))->0, i= 0,1, which split, where K denotes the compact ideal and T*X' the cotangent bundle of the interior of X. Using only simple K-theoretic arguments and the Atiyah-Singer Index Theorem, we show that the Fredholm index of an elliptic element in A is given as the composition of the topological index with mapping K_1(A/K)->K_0(C_0(T*X')) defined above. This relation was first established by Boutet de Monvel by different methods.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7d529bc53f4bd14d781423c6c37d1d84" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630565,"asset_id":20923957,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630565/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923957"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923957"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923957; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923957]").text(description); $(".js-view-count[data-work-id=20923957]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923957; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923957']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "7d529bc53f4bd14d781423c6c37d1d84" } } $('.js-work-strip[data-work-id=20923957]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923957,"title":"A K -theoretic proof of Boutet de Monvel's index theorem for boundary value problems","internal_url":"https://www.academia.edu/20923957/A_K_theoretic_proof_of_Boutet_de_Monvels_index_theorem_for_boundary_value_problems","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630565,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630565/thumbnails/1.jpg","file_name":"0403059.pdf","download_url":"https://www.academia.edu/attachments/41630565/download_file","bulk_download_file_name":"A_K_theoretic_proof_of_Boutet_de_Monvels.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630565/0403059-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DA_K_theoretic_proof_of_Boutet_de_Monvels.pdf\u0026Expires=1740059534\u0026Signature=C5AQzGzw8ZwsTFv1k~Ox18gSEsC1a1b0WebBScK9HDs9phmRn7NibNvZIYWo~oJGKpG1WvmHeOfO55Tz8yuKfsX84nlxz7P73Z0rTnz22I~aEO3ENAQiJj-RhPcRvngA4xWJsSu02VzErY64IvB33VGTCkPs1dfKroKvP~HA~VzLdrTLV74eFSc8fzeZXWMCj1gwAfir7CXb-QdUVvKSuj~yWau6uLUu-IgG923iNfg7TEKkGjgHIII1VcoPofRrPsrEANt~SnaxIg~DExN6HoSD4lRulFA-eK4TNbr2v1eoNmHvFAY8Pedvx6FaeQDht9Pn1oqfiJryFD3aOUqabQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":41630566,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630566/thumbnails/1.jpg","file_name":"0403059.pdf","download_url":"https://www.academia.edu/attachments/41630566/download_file","bulk_download_file_name":"A_K_theoretic_proof_of_Boutet_de_Monvels.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630566/0403059-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DA_K_theoretic_proof_of_Boutet_de_Monvels.pdf\u0026Expires=1740059534\u0026Signature=RsOfr2zv5bZPOpGABRt2kTBVSHQs52cRW1sPsR14-ristSJQaIohhhUsfuCCRm0LkzzxKkFAWunK10gsMOMEMgfonM5qcSWTLivsvDYXWbEuXGdCFa5CsK8OtzBCar7RdC5SK8A94NkFno8TsveHS-Y6cAzO~~yBsdmPwR5~Ty1ONPtHom5ddPCV0yjqmA5Api-81254pdPLTB-WHx-EueD9UF4eOW3B3JRHQJsufI2vjtizZW0IvCTFsHOgj85LIr9EagXjFPta3V1hMoojqNLaqhJfEjEU2KUZlOLI5riXSyf-qv8~FHyO8j8ETmLJKYWzb4TP3S0GvvlKIZMt8w__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923956"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923956/Real_versus_complex_K_theory_using_Kasparovs_bivariant_KK_theory"><img alt="Research paper thumbnail of Real versus complex K�theory using Kasparov's bivariant KK�theory" class="work-thumbnail" src="https://attachments.academia-assets.com/41630561/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923956/Real_versus_complex_K_theory_using_Kasparovs_bivariant_KK_theory">Real versus complex K�theory using Kasparov's bivariant KK�theory</a></div><div class="wp-workCard_item"><span>Algebr Geom Topol</span><span>, 2004</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-th...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C^*-algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the Baum-Connes conjecture for a discrete group to its complex counterpart. In particular, the complex Baum-Connes assembly map is an isomorphism if and only if the real one is, thus reproving a result of Baum and Karoubi. After inverting 2, the same is true for the injectivity or surjectivity part alone.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1c2d40c766bd65234667f3fb79921340" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630561,"asset_id":20923956,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630561/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923956"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923956"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923956; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923956]").text(description); $(".js-view-count[data-work-id=20923956]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923956; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923956']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "1c2d40c766bd65234667f3fb79921340" } } $('.js-work-strip[data-work-id=20923956]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923956,"title":"Real versus complex K�theory using Kasparov's bivariant KK�theory","internal_url":"https://www.academia.edu/20923956/Real_versus_complex_K_theory_using_Kasparovs_bivariant_KK_theory","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630561,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630561/thumbnails/1.jpg","file_name":"0311295.pdf","download_url":"https://www.academia.edu/attachments/41630561/download_file","bulk_download_file_name":"Real_versus_complex_K_theory_using_Kaspa.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630561/0311295-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DReal_versus_complex_K_theory_using_Kaspa.pdf\u0026Expires=1740059534\u0026Signature=TQr7ZkNNnRou6hjB1Za0t~YloWYQ-GREdNPu7uLPJ1x43CXEYEWO3IvtKL6jZcoTr8zTovzlWc7dYTJrq7X5t3rEpJm-AOp979ys5SAOkrP4bCikwgjVqhSUybtfU~GFcji~XChKHflFDu4gVrwMCJsHC9ksWP8jJpzv6iqsEF5m7KMJJfIKF1YIrcijFWR3f0KIA5dxFnygDmLR-LNiNaDrVq46oDqum9Sj~2GqlEmZxB-Uu6gNJXac7toobKD7~SAOKSpxj9ryxaJ9az3TDl-82UHuDx-0mPGgKmH97r~1SvTVEyNZMBEORaq6azt~W7mhjHGMnL0BH00YPp9vgQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923955"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923955/Large_time_limit_and_local_L_2_index_theorems_for_families"><img alt="Research paper thumbnail of Large time limit and local L^2-index theorems for families" class="work-thumbnail" src="https://attachments.academia-assets.com/41630562/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923955/Large_time_limit_and_local_L_2_index_theorems_for_families">Large time limit and local L^2-index theorems for families</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We compute explicitly, and without any extra regularity assumptions, the large time limit of the ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We compute explicitly, and without any extra regularity assumptions, the large time limit of the fibrewise heat operator for Bismut-Lott type superconnections in the L^2-setting. This is motivated by index theory on certain non-compact spaces (families of manifolds with cocompact group action) where the convergence of the heat operator at large time implies refined L^2-index formulas. As applications, we prove a local L^2-index theorem for families of signature operators and an L^2-Bismut-Lott theorem, expressing the Becker-Gottlieb transfer of flat bundles in terms of Kamber-Tandeur classes. With slightly stronger regularity we obtain the respective refined versions: we construct L^2-eta forms and L^2-torsion forms as transgression forms.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="92b287cb8de180e42eb47c2308457ab1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630562,"asset_id":20923955,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630562/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923955"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923955"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923955; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923955]").text(description); $(".js-view-count[data-work-id=20923955]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923955; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923955']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "92b287cb8de180e42eb47c2308457ab1" } } $('.js-work-strip[data-work-id=20923955]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923955,"title":"Large time limit and local L^2-index theorems for families","internal_url":"https://www.academia.edu/20923955/Large_time_limit_and_local_L_2_index_theorems_for_families","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630562,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630562/thumbnails/1.jpg","file_name":"1306.5659.pdf","download_url":"https://www.academia.edu/attachments/41630562/download_file","bulk_download_file_name":"Large_time_limit_and_local_L_2_index_the.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630562/1306.5659-libre.pdf?1453898587=\u0026response-content-disposition=attachment%3B+filename%3DLarge_time_limit_and_local_L_2_index_the.pdf\u0026Expires=1740059534\u0026Signature=WwK~lxny6i8UQkYYIwF9hZaFmijUJq58iFjAoOsaLVdoun2x1m8Vf6EgtX9N~oMePjqcFVFxrZMCuHzKk1G5-0-fsmJY9MGg3v6IPxIqf82hrrtXWL6FMCkvlK4kDedhB36CHmcru1g2UPkB8S3CLzaA~xvqyp0w1QJqUea3PsNtpwDDxsP4n1U7VJH7miF6DTjhK6Xddr4Klx8UAcIJPHfPuRH0XhZEn-uS7MWhXEuE4E0-ebE2Raa8DPCiZpkaMaDNuJYBk8DYKIHHesHMjmf5MR8q98phHSZgUh83RdWBupKAod~lN~fTwkPJB40lTBArh9FJnrPYVTBehm9jWQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":41630563,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630563/thumbnails/1.jpg","file_name":"1306.5659.pdf","download_url":"https://www.academia.edu/attachments/41630563/download_file","bulk_download_file_name":"Large_time_limit_and_local_L_2_index_the.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630563/1306.5659-libre.pdf?1453898589=\u0026response-content-disposition=attachment%3B+filename%3DLarge_time_limit_and_local_L_2_index_the.pdf\u0026Expires=1740059534\u0026Signature=MvsilIVh5Olc08Su5asqcmvpUx7BZeGhZPF2~ywuSRgSeMCHAElQ-mdKNc5EGMvEyGKbs23lfBUsuidr35a7eKdeIFd5KC3tR8w2idyv2mWW-Kjgf~Gb74HX-hoDVTmHYRhOflWhQLg1EjRkjNcZhVf2R5eJnyu9NvOwk-1kZxA2MDLTQq62zm8EgFf~hnWUEpFinWjkfzxpLXHX8ZbzVi7wc-9aROryUW2StTJJOXwwEDBtwTlkiLeXMzTZhQN1n9LHp-1due~qCbMbwJjoRqiE-ZdjkqfjeI~cc-MlNDcXIXE1IknKngyRaWkRxauNXa35jew0ku~tQOKMfPw0sw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923954"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/20923954/Loop_groups_and_string_topology_Lectures_for_the_summer_school_algebraic_groups_Gottingen_July_2005"><img alt="Research paper thumbnail of Loop groups and string topology Lectures for the summer school algebraic groups Gottingen, July 2005" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/20923954/Loop_groups_and_string_topology_Lectures_for_the_summer_school_algebraic_groups_Gottingen_July_2005">Loop groups and string topology Lectures for the summer school algebraic groups Gottingen, July 2005</a></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923954"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923954"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923954; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923954]").text(description); $(".js-view-count[data-work-id=20923954]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923954; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923954']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=20923954]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923954,"title":"Loop groups and string topology Lectures for the summer school algebraic groups Gottingen, July 2005","internal_url":"https://www.academia.edu/20923954/Loop_groups_and_string_topology_Lectures_for_the_summer_school_algebraic_groups_Gottingen_July_2005","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923953"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923953/The_strong_Atiyah_conjecture_for_right_angled_Artin_and_Coxeter_groups"><img alt="Research paper thumbnail of The strong Atiyah conjecture for right-angled Artin and Coxeter groups" class="work-thumbnail" src="https://attachments.academia-assets.com/41630560/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923953/The_strong_Atiyah_conjecture_for_right_angled_Artin_and_Coxeter_groups">The strong Atiyah conjecture for right-angled Artin and Coxeter groups</a></div><div class="wp-workCard_item"><span>Geom Dedic</span><span>, Oct 4, 2010</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter grou...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter groups. More generally, we prove it for groups which are certain finite extensions or elementary amenable extensions of such groups.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="c7f9568073a088582f0a93d8b7367229" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630560,"asset_id":20923953,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630560/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923953"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923953"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923953; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923953]").text(description); $(".js-view-count[data-work-id=20923953]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923953; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923953']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "c7f9568073a088582f0a93d8b7367229" } } $('.js-work-strip[data-work-id=20923953]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923953,"title":"The strong Atiyah conjecture for right-angled Artin and Coxeter groups","internal_url":"https://www.academia.edu/20923953/The_strong_Atiyah_conjecture_for_right_angled_Artin_and_Coxeter_groups","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630560,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630560/thumbnails/1.jpg","file_name":"1010.0606.pdf","download_url":"https://www.academia.edu/attachments/41630560/download_file","bulk_download_file_name":"The_strong_Atiyah_conjecture_for_right_a.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630560/1010.0606-libre.pdf?1453898585=\u0026response-content-disposition=attachment%3B+filename%3DThe_strong_Atiyah_conjecture_for_right_a.pdf\u0026Expires=1740046991\u0026Signature=W3CATHtCpH32cG3Y0ntSrebeBUSV-4iqAV4pajRfTXFirZeFTrA5UfM4h74gPfVGw1xQDrKxohb05y6xWSKvxHu4tHPLZ00tbYxM5v2KXDj3y4vFCdkPhLg6Iur0jX~no8O5PwBRnwYjnMWuxiotQS5ETWWfmtbhoPLA-qoDyW7QgFIUeXoR0~oAqKQTYvrtU3dBNolEdIiuK6bsfEhJ8aP59MrE8wtsph2TE-HxgWBjM2gRiFJjiP9KHYX-7wGaXwgCdmfSWtWA94ONn~HZueKk760uXsxSJDYrRvAiwvztIzSzBAdFwzLGDOIeoLiXWNPxN19bkdomABKSsrM7XA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923952"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923952/Buildings_have_finite_asymptotic_dimension"><img alt="Research paper thumbnail of Buildings have finite asymptotic dimension" class="work-thumbnail" src="https://attachments.academia-assets.com/41630675/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923952/Buildings_have_finite_asymptotic_dimension">Buildings have finite asymptotic dimension</a></div><div class="wp-workCard_item"><span>Russian Journal of Mathematical Physics</span><span>, Sep 12, 2009</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">It is proved that the asymptotic dimension of any building is finite and equal to the asymptotic ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">It is proved that the asymptotic dimension of any building is finite and equal to the asymptotic dimension of an apartment in that building.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="03981a3d5edf18c89f48bf2ebb465b5d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630675,"asset_id":20923952,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630675/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923952"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923952"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923952; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923952]").text(description); $(".js-view-count[data-work-id=20923952]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923952; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923952']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "03981a3d5edf18c89f48bf2ebb465b5d" } } $('.js-work-strip[data-work-id=20923952]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923952,"title":"Buildings have finite asymptotic dimension","internal_url":"https://www.academia.edu/20923952/Buildings_have_finite_asymptotic_dimension","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630675,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630675/thumbnails/1.jpg","file_name":"Buildings_have_finite_asymptotic_dimensi20160127-21972-102nptw.pdf","download_url":"https://www.academia.edu/attachments/41630675/download_file","bulk_download_file_name":"Buildings_have_finite_asymptotic_dimensi.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630675/Buildings_have_finite_asymptotic_dimensi20160127-21972-102nptw-libre.pdf?1453898568=\u0026response-content-disposition=attachment%3B+filename%3DBuildings_have_finite_asymptotic_dimensi.pdf\u0026Expires=1740046991\u0026Signature=LQ7uNpV6F2ZrFmaa7blONiV7jm9b3VPGSD1zkb300T7aIaeMPLgYKpOoCFqQVZ5qMI-gL2-BfDTDZ60m712XMZ3932VODWb1F~MZtUQHhKad9JtiAtibDDi5XskmkAOxhf7dNK2N8kXwdH-NPeVTGcqNhS72UN4xi26hCDM1GN45B3~DcHPixvUhdMcsJGkkpkLngzhhNpPM1oYnipbO16CDktaEm1hyUblv3OYL~9w~4OrNQuueVXvURVW6GlL4B6PqrW6ckjBx7-rfkM~txhuaZLRBbcxQlXk~IGFM4DgoDAJeTIV~fTa7oEWX4jl8dH6qr~xd7c9GK-BNL06gEg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923951"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923951/Bordism_rho_invariants_and_the_Baum_Connes_conjecture"><img alt="Research paper thumbnail of Bordism, rho-invariants and the Baum-Connes conjecture" class="work-thumbnail" src="https://attachments.academia-assets.com/41630668/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923951/Bordism_rho_invariants_and_the_Baum_Connes_conjecture">Bordism, rho-invariants and the Baum-Connes conjecture</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let G be a finitely generated discrete group. In this paper we establish vanishing results for rh...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let G be a finitely generated discrete group. In this paper we establish vanishing results for rho-invariants associated to (i) the spin-Dirac operator of a spin manifold with positive scalar curvature (ii) the signature operator of the disjoint union of a pair of homotopy equivalent oriented manifolds with fundamental group G. The invariants we consider are more precisely - the Atiyah-Patodi-Singer rho-invariant associated to a pair of finite dimensional unitary representations. - the L2-rho invariant of Cheeger-Gromov - the delocalized eta invariant of Lott for a finite conjugacy class of G. We prove that all these rho-invariants vanish if the group G is torsion-free and the Baum-Connes map for the maximal group C^*-algebra is bijective. For the delocalized invariant we only assume the validity of the Baum-Connes conjecture for the reduced C^*-algebra. In particular, the three rho-invariants associated to the signature operator are, for such groups, homotopy invariant. For the APS and the Cheeger-Gromov rho-invariants the latter result had been established by Navin Keswani. Our proof re-establishes this result and also extends it to the delocalized eta-invariant of Lott. Our method also gives some information about the eta-invariant itself (a much more saddle object than the rho-invariant).</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7a83ce4a538f13f8e9b945f334dd37dd" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630668,"asset_id":20923951,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630668/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923951"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923951"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923951; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923951]").text(description); $(".js-view-count[data-work-id=20923951]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923951; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923951']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "7a83ce4a538f13f8e9b945f334dd37dd" } } $('.js-work-strip[data-work-id=20923951]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923951,"title":"Bordism, rho-invariants and the Baum-Connes conjecture","internal_url":"https://www.academia.edu/20923951/Bordism_rho_invariants_and_the_Baum_Connes_conjecture","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630668,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630668/thumbnails/1.jpg","file_name":"Bordism_rho_invariants_and_the_Baum-Connes_conjecture_final_published_ante_proofreading.pdf","download_url":"https://www.academia.edu/attachments/41630668/download_file","bulk_download_file_name":"Bordism_rho_invariants_and_the_Baum_Conn.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630668/Bordism_rho_invariants_and_the_Baum-Connes_conjecture_final_published_ante_proofreading-libre.pdf?1453898587=\u0026response-content-disposition=attachment%3B+filename%3DBordism_rho_invariants_and_the_Baum_Conn.pdf\u0026Expires=1740059534\u0026Signature=ETOhBpK4kDoJad4WLFmh0Tk4ZuIhksQ0Ry9mO0a47ubbHSR82jGDZ36rwl3gjGki30EMvnJQDLky09dC~IyzFxY-KpJJQtsQd4MUBcYc5N5AQ1WjfqZuZyupQVwa625v1kDPmVhlh2KjyZOgl4KaBW34BrZ8ELKRu1~pzfp6rKggVizsZ0O~K31Ve9uY2H9ZJUPIAkTVk5nO2W2NeYtWkB2b2rBksC5kPFP391wJqvEoxOBj8VQyd~HK9tUP9YBKC6WVkq0NyOlkGOZZggaZt0e57ZsvRyZ51haRJYJUj-UkGqXWploXSZyK68qItB7pJ2YYZHZVnPxuvce4wh5AgA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923950"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923950/Duality_for_topological_abelian_group_stacks_and_T_duality"><img alt="Research paper thumbnail of Duality for topological abelian group stacks and T-duality" class="work-thumbnail" src="https://attachments.academia-assets.com/41630558/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923950/Duality_for_topological_abelian_group_stacks_and_T_duality">Duality for topological abelian group stacks and T-duality</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">v2: An additional assumption was added in Theorem 4.8. In order to show that a connected abelian ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">v2: An additional assumption was added in Theorem 4.8. In order to show that a connected abelian group is admissible on the site of locally compact spaces we must in addition assume that it is locally topologically divisible. This condition is used in the proof of Lemma 4.62.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="dfb111dcea0f4822c71efc54a098dae1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630558,"asset_id":20923950,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630558/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923950"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923950"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923950; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923950]").text(description); $(".js-view-count[data-work-id=20923950]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923950; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923950']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "dfb111dcea0f4822c71efc54a098dae1" } } $('.js-work-strip[data-work-id=20923950]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923950,"title":"Duality for topological abelian group stacks and T-duality","internal_url":"https://www.academia.edu/20923950/Duality_for_topological_abelian_group_stacks_and_T_duality","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630558,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630558/thumbnails/1.jpg","file_name":"0701428.pdf","download_url":"https://www.academia.edu/attachments/41630558/download_file","bulk_download_file_name":"Duality_for_topological_abelian_group_st.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630558/0701428-libre.pdf?1453898597=\u0026response-content-disposition=attachment%3B+filename%3DDuality_for_topological_abelian_group_st.pdf\u0026Expires=1740059534\u0026Signature=TavBJM8fH7PuD6rZt9HX5seVF0wOWjWSGJEhFr~UoC6vUky8UJftFIu6AqWno9mZErShwnO0L~bdc9qvd9k8CXMgcoauXbOltuTgzjoh4mr17cnVtnuvXVKGU7wBamjDbcA3ife1S4zpPl8YvjeVqlhQLhXIg0jayPymPHe5fRidkGjElU7Aq3MAdcCmow1UHLJg6lp2hDInNOc~tJJnUzo3JO1HO67tVmWTpRa-fwpRqx6j8B0Dn1i~t2tIDx2KSlKp3dQzCjENdrwH9tVPf45B6GDvniCzTyPUPoS9smNlfUsxycxw0COYH172JIIYu9ZnDSd6uYi3N8bzqdUmYA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":41630557,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630557/thumbnails/1.jpg","file_name":"0701428.pdf","download_url":"https://www.academia.edu/attachments/41630557/download_file","bulk_download_file_name":"Duality_for_topological_abelian_group_st.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630557/0701428-libre.pdf?1453898597=\u0026response-content-disposition=attachment%3B+filename%3DDuality_for_topological_abelian_group_st.pdf\u0026Expires=1740059534\u0026Signature=bYqJx8h07gG1sgEbJKMg6vAsUMMXKbsaNw2I1y4a-ewUw5AoRhjEBfCbpz8rlJmoMqWMx-sY181ooH-ailzyhqJdtMVNM1fS0IA22KVGoFPD8CDrnbYTW6SeK~njppWn7zXvgLJ4oCu0MV8OFGrdrDb0KCEknuVoise-8KO9S1ySsHWhQ387UhMj-JvxU2yrhvfhtICytaGWT0-aL8MD2lh3MCSae~bNVrECjQGj4edyjN2PG7w0LZCm-~aEXxCfsiukppRXeS5MgkkiaALmY8k3-60uQMee2-6PS~9n7-czTOjnIYU8xa7pWTsJszVVDiagnPyXym375nqsOVOL2A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20923949"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20923949/Various_L_2_signatures_and_a_topological_L_2_signature_theorem"><img alt="Research paper thumbnail of Various L 2 -signatures and a topological L 2 -signature theorem" class="work-thumbnail" src="https://attachments.academia-assets.com/41630670/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20923949/Various_L_2_signatures_and_a_topological_L_2_signature_theorem">Various L 2 -signatures and a topological L 2 -signature theorem</a></div><div class="wp-workCard_item"><span>High-Dimensional Manifold Topology</span><span>, 2003</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">For a normal covering over a closed oriented topological manifold we give a proof of the L 2 -sig...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">For a normal covering over a closed oriented topological manifold we give a proof of the L 2 -signature theorem with twisted coefficients, using Lipschitz structures and the Lipschitz signature operator introduced by Teleman. We also prove that the L-theory isomorphism conjecture as well as the C * max -version of the Baum-Connes conjecture imply the L 2signature theorem for a normal covering over a Poincaré space, provided that the group of deck transformations is torsion-free.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="74880b3084550204238edee0f9fefe46" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41630670,"asset_id":20923949,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41630670/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20923949"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20923949"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20923949; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20923949]").text(description); $(".js-view-count[data-work-id=20923949]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20923949; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20923949']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "74880b3084550204238edee0f9fefe46" } } $('.js-work-strip[data-work-id=20923949]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20923949,"title":"Various L 2 -signatures and a topological L 2 -signature theorem","internal_url":"https://www.academia.edu/20923949/Various_L_2_signatures_and_a_topological_L_2_signature_theorem","owner_id":35644036,"coauthors_can_edit":true,"owner":{"id":35644036,"first_name":"Thomas","middle_initials":"","last_name":"Schick","page_name":"TSchick","domain_name":"uni-goettingen","created_at":"2015-10-04T15:05:38.825-07:00","display_name":"Thomas Schick","url":"https://uni-goettingen.academia.edu/TSchick"},"attachments":[{"id":41630670,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41630670/thumbnails/1.jpg","file_name":"Various_L2-signatures_and_a_topological_20160127-16054-1xnvt88.pdf","download_url":"https://www.academia.edu/attachments/41630670/download_file","bulk_download_file_name":"Various_L_2_signatures_and_a_topological.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41630670/Various_L2-signatures_and_a_topological_20160127-16054-1xnvt88-libre.pdf?1453898571=\u0026response-content-disposition=attachment%3B+filename%3DVarious_L_2_signatures_and_a_topological.pdf\u0026Expires=1740059534\u0026Signature=G7XQKYRW77omN3FtWEkCWpzrX7Jy54NeLVaJtHBzPg3-pjzadLfeQv15Bdk~ikUaB6CafceaOczNEZ3CfIKvlOgm-5xBsuv-CWrQNvx09kPnpuxc5bvUzy3d24QopelnGwRCH3aCl5ed3Duss1k8S8aRUVMkE-uGKz4WBgdYE3OQRM5HuNnv39buM6N4QrhJ0kp52ikn3GTfvqyNM-jyZ4ax2bPFg0nz681UDhy5ryVTlkGfWx8K1tzqXXok~zYDq9yvo-8xsu3D4YM5sUsmlbUF6z94SLHClQj-MZKVR9DwHh7uiBDIxIyy4NGEGMyryzO8f3Bo83IR0nyDTxVi2Q__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/google_contacts-0dfb882d836b94dbcb4a2d123d6933fc9533eda5be911641f20b4eb428429600.js"], function() { // from javascript_helper.rb $('.js-google-connect-button').click(function(e) { e.preventDefault(); GoogleContacts.authorize_and_show_contacts(); Aedu.Dismissibles.recordClickthrough("WowProfileImportContactsPrompt"); }); $('.js-update-biography-button').click(function(e) { e.preventDefault(); Aedu.Dismissibles.recordClickthrough("UpdateUserBiographyPrompt"); $.ajax({ url: $r.api_v0_profiles_update_about_path({ subdomain_param: 'api', about: "", }), type: 'PUT', success: function(response) { location.reload(); } }); }); $('.js-work-creator-button').click(function (e) { e.preventDefault(); window.location = $r.upload_funnel_document_path({ source: encodeURIComponent(""), }); }); $('.js-video-upload-button').click(function (e) { e.preventDefault(); window.location = $r.upload_funnel_video_path({ source: encodeURIComponent(""), }); }); $('.js-do-this-later-button').click(function() { $(this).closest('.js-profile-nag-panel').remove(); Aedu.Dismissibles.recordDismissal("WowProfileImportContactsPrompt"); }); $('.js-update-biography-do-this-later-button').click(function(){ $(this).closest('.js-profile-nag-panel').remove(); Aedu.Dismissibles.recordDismissal("UpdateUserBiographyPrompt"); }); $('.wow-profile-mentions-upsell--close').click(function(){ $('.wow-profile-mentions-upsell--panel').hide(); Aedu.Dismissibles.recordDismissal("WowProfileMentionsUpsell"); }); $('.wow-profile-mentions-upsell--button').click(function(){ Aedu.Dismissibles.recordClickthrough("WowProfileMentionsUpsell"); }); new WowProfile.SocialRedesignUserWorks({ initialWorksOffset: 20, allWorksOffset: 20, maxSections: 1 }) }); </script> </div></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile_edit-5ea339ee107c863779f560dd7275595239fed73f1a13d279d2b599a28c0ecd33.js","https://a.academia-assets.com/assets/add_coauthor-22174b608f9cb871d03443cafa7feac496fb50d7df2d66a53f5ee3c04ba67f53.js","https://a.academia-assets.com/assets/tab-dcac0130902f0cc2d8cb403714dd47454f11fc6fb0e99ae6a0827b06613abc20.js","https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js"], function() { // from javascript_helper.rb window.ae = window.ae || {}; window.ae.WowProfile = window.ae.WowProfile || {}; if(Aedu.User.current && Aedu.User.current.id === $viewedUser.id) { window.ae.WowProfile.current_user_edit = {}; new WowProfileEdit.EditUploadView({ el: '.js-edit-upload-button-wrapper', model: window.$current_user, }); new AddCoauthor.AddCoauthorsController(); } var userInfoView = new WowProfile.SocialRedesignUserInfo({ recaptcha_key: "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB" }); WowProfile.router = new WowProfile.Router({ userInfoView: userInfoView }); Backbone.history.start({ pushState: true, root: "/" + $viewedUser.page_name }); new WowProfile.UserWorksNav() }); </script> </div> <div class="bootstrap login"><div class="modal fade login-modal" id="login-modal"><div class="login-modal-dialog modal-dialog"><div class="modal-content"><div class="modal-header"><button class="close close" data-dismiss="modal" type="button"><span aria-hidden="true">×</span><span class="sr-only">Close</span></button><h4 class="modal-title text-center"><strong>Log In</strong></h4></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><button class="btn btn-fb btn-lg btn-block btn-v-center-content" id="login-facebook-oauth-button"><svg style="float: left; width: 19px; line-height: 1em; margin-right: .3em;" aria-hidden="true" focusable="false" data-prefix="fab" data-icon="facebook-square" class="svg-inline--fa fa-facebook-square fa-w-14" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><path fill="currentColor" d="M400 32H48A48 48 0 0 0 0 80v352a48 48 0 0 0 48 48h137.25V327.69h-63V256h63v-54.64c0-62.15 37-96.48 93.67-96.48 27.14 0 55.52 4.84 55.52 4.84v61h-31.27c-30.81 0-40.42 19.12-40.42 38.73V256h68.78l-11 71.69h-57.78V480H400a48 48 0 0 0 48-48V80a48 48 0 0 0-48-48z"></path></svg><small><strong>Log in</strong> with <strong>Facebook</strong></small></button><br /><button class="btn btn-google btn-lg btn-block btn-v-center-content" id="login-google-oauth-button"><svg style="float: left; width: 22px; line-height: 1em; margin-right: .3em;" aria-hidden="true" focusable="false" data-prefix="fab" data-icon="google-plus" class="svg-inline--fa fa-google-plus fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M256,8C119.1,8,8,119.1,8,256S119.1,504,256,504,504,392.9,504,256,392.9,8,256,8ZM185.3,380a124,124,0,0,1,0-248c31.3,0,60.1,11,83,32.3l-33.6,32.6c-13.2-12.9-31.3-19.1-49.4-19.1-42.9,0-77.2,35.5-77.2,78.1S142.3,334,185.3,334c32.6,0,64.9-19.1,70.1-53.3H185.3V238.1H302.2a109.2,109.2,0,0,1,1.9,20.7c0,70.8-47.5,121.2-118.8,121.2ZM415.5,273.8v35.5H380V273.8H344.5V238.3H380V202.8h35.5v35.5h35.2v35.5Z"></path></svg><small><strong>Log in</strong> with <strong>Google</strong></small></button><br /><style type="text/css">.sign-in-with-apple-button { width: 100%; height: 52px; border-radius: 3px; border: 1px solid black; cursor: pointer; } .sign-in-with-apple-button > div { margin: 0 auto; / This centers the Apple-rendered button horizontally }</style><script src="https://appleid.cdn-apple.com/appleauth/static/jsapi/appleid/1/en_US/appleid.auth.js" type="text/javascript"></script><div class="sign-in-with-apple-button" data-border="false" data-color="white" id="appleid-signin"><span   ="Sign Up with Apple" class="u-fs11"></span></div><script>AppleID.auth.init({ clientId: 'edu.academia.applesignon', scope: 'name email', redirectURI: 'https://www.academia.edu/sessions', state: "e7ae54d12cd80f3d6f1ba6abf21fc47843671825fad94e85242a107f1ea45f83", });</script><script>// Hacky way of checking if on fast loswp if (window.loswp == null) { (function() { const Google = window?.Aedu?.Auth?.OauthButton?.Login?.Google; const Facebook = window?.Aedu?.Auth?.OauthButton?.Login?.Facebook; if (Google) { new Google({ el: '#login-google-oauth-button', rememberMeCheckboxId: 'remember_me', track: null }); } if (Facebook) { new Facebook({ el: '#login-facebook-oauth-button', rememberMeCheckboxId: 'remember_me', track: null }); } })(); }</script></div></div></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><div class="hr-heading login-hr-heading"><span class="hr-heading-text">or</span></div></div></div></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><form class="js-login-form" action="https://www.academia.edu/sessions" accept-charset="UTF-8" method="post"><input type="hidden" name="authenticity_token" value="VOGxLURXEnC-x0_C006AwgmM7GlFdPgZ-od_fgKHqQ3AQtvhETMAgphA3indnGqKDi1INZKRBnvalXqjHdWJ_w" autocomplete="off" /><div class="form-group"><label class="control-label" for="login-modal-email-input" style="font-size: 14px;">Email</label><input class="form-control" id="login-modal-email-input" name="login" type="email" /></div><div class="form-group"><label class="control-label" for="login-modal-password-input" style="font-size: 14px;">Password</label><input class="form-control" id="login-modal-password-input" name="password" type="password" /></div><input type="hidden" name="post_login_redirect_url" id="post_login_redirect_url" value="https://uni-goettingen.academia.edu/TSchick" autocomplete="off" /><div class="checkbox"><label><input type="checkbox" name="remember_me" id="remember_me" value="1" checked="checked" /><small style="font-size: 12px; margin-top: 2px; display: inline-block;">Remember me on this computer</small></label></div><br><input type="submit" name="commit" value="Log In" class="btn btn-primary btn-block btn-lg js-login-submit" data-disable-with="Log In" /></br></form><script>typeof window?.Aedu?.recaptchaManagedForm === 'function' && window.Aedu.recaptchaManagedForm( document.querySelector('.js-login-form'), document.querySelector('.js-login-submit') );</script><small style="font-size: 12px;"><br />or <a data-target="#login-modal-reset-password-container" data-toggle="collapse" href="javascript:void(0)">reset password</a></small><div class="collapse" id="login-modal-reset-password-container"><br /><div class="well margin-0x"><form class="js-password-reset-form" action="https://www.academia.edu/reset_password" accept-charset="UTF-8" method="post"><input type="hidden" name="authenticity_token" value="9jjgYD66mnZ2hALWg5BUYHw7_sdozHceXGHenVVs3ztim4qsa96IhFADkz2NQr4oe5pam78piXx8c9tASj7_yQ" autocomplete="off" /><p>Enter the email address you signed up with and we'll email you a reset link.</p><div class="form-group"><input class="form-control" name="email" type="email" /></div><script src="https://recaptcha.net/recaptcha/api.js" async defer></script> <script> var invisibleRecaptchaSubmit = function () { var closestForm = function (ele) { var curEle = ele.parentNode; while (curEle.nodeName !== 'FORM' && curEle.nodeName !== 'BODY'){ curEle = curEle.parentNode; } return curEle.nodeName === 'FORM' ? curEle : null }; var eles = document.getElementsByClassName('g-recaptcha'); if (eles.length > 0) { var form = closestForm(eles[0]); if (form) { form.submit(); } } }; </script> <input type="submit" data-sitekey="6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj" data-callback="invisibleRecaptchaSubmit" class="g-recaptcha btn btn-primary btn-block" value="Email me a link" value=""/> </form></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/collapse-45805421cf446ca5adf7aaa1935b08a3a8d1d9a6cc5d91a62a2a3a00b20b3e6a.js"], function() { // from javascript_helper.rb $("#login-modal-reset-password-container").on("shown.bs.collapse", function() { $(this).find("input[type=email]").focus(); }); }); </script> </div></div></div><div class="modal-footer"><div class="text-center"><small style="font-size: 12px;">Need an account? <a rel="nofollow" href="https://www.academia.edu/signup">Click here to sign up</a></small></div></div></div></div></div></div><script>// If we are on subdomain or non-bootstrapped page, redirect to login page instead of showing modal (function(){ if (typeof $ === 'undefined') return; var host = window.location.hostname; if ((host === $domain || host === "www."+$domain) && (typeof $().modal === 'function')) { $("#nav_log_in").click(function(e) { // Don't follow the link and open the modal e.preventDefault(); $("#login-modal").on('shown.bs.modal', function() { $(this).find("#login-modal-email-input").focus() }).modal('show'); }); } })()</script> <div class="bootstrap" id="footer"><div class="footer-content clearfix text-center padding-top-7x" style="width:100%;"><ul class="footer-links-secondary footer-links-wide list-inline margin-bottom-1x"><li><a href="https://www.academia.edu/about">About</a></li><li><a href="https://www.academia.edu/press">Press</a></li><li><a href="https://www.academia.edu/documents">Papers</a></li><li><a href="https://www.academia.edu/topics">Topics</a></li><li><a href="https://www.academia.edu/journals">Academia.edu Journals</a></li><li><a rel="nofollow" href="https://www.academia.edu/hiring"><svg style="width: 13px; height: 13px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="briefcase" class="svg-inline--fa fa-briefcase fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M320 336c0 8.84-7.16 16-16 16h-96c-8.84 0-16-7.16-16-16v-48H0v144c0 25.6 22.4 48 48 48h416c25.6 0 48-22.4 48-48V288H320v48zm144-208h-80V80c0-25.6-22.4-48-48-48H176c-25.6 0-48 22.4-48 48v48H48c-25.6 0-48 22.4-48 48v80h512v-80c0-25.6-22.4-48-48-48zm-144 0H192V96h128v32z"></path></svg> <strong>We're Hiring!</strong></a></li><li><a rel="nofollow" href="https://support.academia.edu/hc/en-us"><svg style="width: 12px; height: 12px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="question-circle" class="svg-inline--fa fa-question-circle fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M504 256c0 136.997-111.043 248-248 248S8 392.997 8 256C8 119.083 119.043 8 256 8s248 111.083 248 248zM262.655 90c-54.497 0-89.255 22.957-116.549 63.758-3.536 5.286-2.353 12.415 2.715 16.258l34.699 26.31c5.205 3.947 12.621 3.008 16.665-2.122 17.864-22.658 30.113-35.797 57.303-35.797 20.429 0 45.698 13.148 45.698 32.958 0 14.976-12.363 22.667-32.534 33.976C247.128 238.528 216 254.941 216 296v4c0 6.627 5.373 12 12 12h56c6.627 0 12-5.373 12-12v-1.333c0-28.462 83.186-29.647 83.186-106.667 0-58.002-60.165-102-116.531-102zM256 338c-25.365 0-46 20.635-46 46 0 25.364 20.635 46 46 46s46-20.636 46-46c0-25.365-20.635-46-46-46z"></path></svg> <strong>Help Center</strong></a></li></ul><ul class="footer-links-tertiary list-inline margin-bottom-1x"><li class="small">Find new research papers in:</li><li class="small"><a href="https://www.academia.edu/Documents/in/Physics">Physics</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Chemistry">Chemistry</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Biology">Biology</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Health_Sciences">Health Sciences</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Ecology">Ecology</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Earth_Sciences">Earth Sciences</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Cognitive_Science">Cognitive Science</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Computer_Science">Computer Science</a></li></ul></div></div><div class="DesignSystem" id="credit" style="width:100%;"><ul class="u-pl0x footer-links-legal list-inline"><li><a rel="nofollow" href="https://www.academia.edu/terms">Terms</a></li><li><a rel="nofollow" href="https://www.academia.edu/privacy">Privacy</a></li><li><a rel="nofollow" href="https://www.academia.edu/copyright">Copyright</a></li><li>Academia ©2025</li></ul></div><script> //<![CDATA[ window.detect_gmtoffset = true; window.Academia && window.Academia.set_gmtoffset && Academia.set_gmtoffset('/gmtoffset'); //]]> </script> <div id='overlay_background'></div> <div id='bootstrap-modal-container' class='bootstrap'></div> <div id='ds-modal-container' class='bootstrap DesignSystem'></div> <div id='full-screen-modal'></div> </div> </body> </html>