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He graduated in 1962 from Norwood, Norfolk High School and earned a BS in Mathematics from MIT in 1966. He received a PhD in Mathematics from Princeton University in 1972. He teaches at the University of Illinois from 1971 to the present time, where is now Professor of Mathematics Emeritus. Kauffman is known for introducing state summations into the theory of invariants of knots, beginning with his model for the Alexander Polynomial and his bracket state summation model for the Jones polynomial. He is know for his discovery of the two-variable Kauffman polynomial and for his discovery and investigation of virtual knot theory. He is the author of four books on the theory of knots and the editor of a number of collections of papers related to knot theory. Kauffman is the Editor in Chief and founding editor of the Journal of Knot Theory and Its Ramifications (JKTR) published by World Scientific. Kauffman is the editor of the Book Series on Knots and Everything published by World Scientific. Kauffman is a Fellow of the American Mathematical Society and a former Polya Lecturer for the Mathematical Society of America. Kauffman is the recipient of the Warren McCulloch Award and the Norbert Wiener Gold Medal of the American Society for Cybernetics. His research interests are in knot theory, quantum theory and the epistemology of form. He writes a regular column on Virtual Logic for the Journal, Cybernetics and Human Knowing. He plays clarinet in the Chicago based ChickenFat Klezmer Orchestra.<br /><span class="u-fw700">Supervisors: </span>Kauffman's PhD advisor is William Browder<br /><span class="u-fw700">Phone: </span>(312)996-3066<br /><b>Address: </b>5530 South Shore Drive, Apt 7C<br />Chicago, IL 60637-1946<br /><div class="js-profile-less-about u-linkUnstyled u-tcGrayDarker u-textDecorationUnderline u-displayNone">less</div></div></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://williams.academia.edu/StevenJMiller"><img class="profile-avatar u-positionAbsolute" alt="Steven J. 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id="social-redesign-work-container"><div class="upload-header"><h2 class="ds2-5-heading-sans-serif-xs">Uploads</h2></div><div class="nav-container backbone-profile-documents-nav hidden-xs"><ul class="nav-tablist" role="tablist"><li class="nav-chip active" role="presentation"><a data-section-name="" data-toggle="tab" href="#all" role="tab">all</a></li><li class="nav-chip" role="presentation"><a class="js-profile-docs-nav-section u-textTruncate" data-click-track="profile-works-tab" data-section-name="Papers" data-toggle="tab" href="#papers" role="tab" title="Papers"><span>605</span> <span class="ds2-5-body-sm-bold">Papers</span></a></li><li class="nav-chip" role="presentation"><a class="js-profile-docs-nav-section u-textTruncate" data-click-track="profile-works-tab" data-section-name="Drafts" data-toggle="tab" href="#drafts" role="tab" title="Drafts"><span>1</span> <span class="ds2-5-body-sm-bold">Drafts</span></a></li></ul></div><div class="divider ds-divider-16" style="margin: 0px;"></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 Louis H Kauffman</h3></div><div class="js-work-strip profile--work_container" data-work-id="126969354"><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/126969354/Knot_Diagrammatics"><img alt="Research paper thumbnail of Knot Diagrammatics" class="work-thumbnail" src="https://attachments.academia-assets.com/120771074/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/126969354/Knot_Diagrammatics">Knot Diagrammatics</a></div><div class="wp-workCard_item"><span>Handbook of Knot Theory</span><span>, 2005</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper is a survey of knot theory and invariants of knots and links from the point of view of...</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">This paper is a survey of knot theory and invariants of knots and links from the point of view of categories of diagrams. The topics range from foundations of knot theory to virtual knot theory and topological quantum field theory.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4bf34bd55a2d17fd744396e3b704fcc5" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":120771074,"asset_id":126969354,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/120771074/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="126969354"><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="126969354"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 126969354; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=126969354]").text(description); $(".js-view-count[data-work-id=126969354]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 126969354; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='126969354']"); 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: "4bf34bd55a2d17fd744396e3b704fcc5" } } $('.js-work-strip[data-work-id=126969354]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":126969354,"title":"Knot Diagrammatics","translated_title":"","metadata":{"publisher":"Elsevier","ai_title_tag":"Knot Diagrams in Knot Theory Survey","grobid_abstract":"This paper is a survey of knot theory and invariants of knots and links from the point of view of categories of diagrams. 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Let n,...</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">Conjecture: Consider an arbitrary closed 3-manifold M, and let X be a special spine for M. Let n, be the number of closed surfaces contained in X that have even Euler characteristic and no the number of closed surfaces in X that have odd Euler characteristic. Then either, nr = ...</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="126243984"><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="126243984"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 126243984; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=126243984]").text(description); $(".js-view-count[data-work-id=126243984]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 126243984; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='126243984']"); 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" } } $('.js-work-strip[data-work-id=126243984]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":126243984,"title":"Computing Turaev-Viro invariants for 3-manifolds","translated_title":"","metadata":{"abstract":"Conjecture: Consider an arbitrary closed 3-manifold M, and let X be a special spine for M. 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</script> <div class="js-work-strip profile--work_container" data-work-id="126243983"><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/126243983/A_State_Sum_Link_Invariant_of_Regular_Isotopy"><img alt="Research paper thumbnail of A State Sum Link Invariant of Regular Isotopy" 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/126243983/A_State_Sum_Link_Invariant_of_Regular_Isotopy">A State Sum Link Invariant of Regular Isotopy</a></div><div class="wp-workCard_item"><span>arXiv (Cornell University)</span><span>, Oct 14, 2007</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT This paper has been withdrawn because there is a fundamental error in the computations; ...</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">ABSTRACT This paper has been withdrawn because there is a fundamental error in the computations; with the right computational scheme it seems to be just a version of the Jones polynomial Comment: This paper has been withdrawn because there is a fundamental error in the computations; with the right computational scheme it seems to be just a version of the Jones polynomial</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="126243983"><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="126243983"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 126243983; 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They outline the measures that enable both media artists and computer scientists to benefit from the collaborations. In particular, if long-term collaborations are to be successful, the collaborators must garner rewards not only in the field of the collaboration but also in their own respective academic or professional fields.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="126243988"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="126243988"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 126243988; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=126243988]").text(description); $(".js-view-count[data-work-id=126243988]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 126243988; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='126243988']"); 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" } } $('.js-work-strip[data-work-id=126243988]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":126243988,"title":"The Artist and the Scientific Research Environment","translated_title":"","metadata":{"abstract":"The authors reflect on the experiences of collaboration between artists and scientists at the Electronic Visualization Laboratory at the University of Illinois at Chicago. 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The 3-Vertex","translated_title":"","metadata":{"publication_date":{"day":31,"month":12,"year":1994,"errors":{}}},"translated_abstract":null,"internal_url":"https://www.academia.edu/126243985/Chapter_4_The_3_Vertex","translated_internal_url":"","created_at":"2024-12-11T06:34:57.126-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":1187729,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Chapter_4_The_3_Vertex","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":null,"owner":{"id":1187729,"first_name":"Louis","middle_initials":null,"last_name":"H Kauffman","page_name":"LouisHKauffman","domain_name":"uic","created_at":"2012-02-07T04:50:11.529-08:00","display_name":"Louis H Kauffman","url":"https://uic.academia.edu/LouisHKauffman"},"attachments":[],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"}],"urls":[{"id":46021451,"url":"https://doi.org/10.1515/9781400882533-004"}]}, 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="126243984"><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/126243984/Computing_Turaev_Viro_invariants_for_3_manifolds"><img alt="Research paper thumbnail of Computing Turaev-Viro invariants for 3-manifolds" 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/126243984/Computing_Turaev_Viro_invariants_for_3_manifolds">Computing Turaev-Viro invariants for 3-manifolds</a></div><div class="wp-workCard_item"><span>Manuscripta Mathematica</span><span>, Dec 1, 1991</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Conjecture: Consider an arbitrary closed 3-manifold M, and let X be a special spine for M. Let n,...</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">Conjecture: Consider an arbitrary closed 3-manifold M, and let X be a special spine for M. Let n, be the number of closed surfaces contained in X that have even Euler characteristic and no the number of closed surfaces in X that have odd Euler characteristic. Then either, nr = ...</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="126243984"><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="126243984"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 126243984; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=126243984]").text(description); $(".js-view-count[data-work-id=126243984]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 126243984; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='126243984']"); 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" } } $('.js-work-strip[data-work-id=126243984]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":126243984,"title":"Computing Turaev-Viro invariants for 3-manifolds","translated_title":"","metadata":{"abstract":"Conjecture: Consider an arbitrary closed 3-manifold M, and let X be a special spine for M. 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</script> <div class="js-work-strip profile--work_container" data-work-id="126243983"><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/126243983/A_State_Sum_Link_Invariant_of_Regular_Isotopy"><img alt="Research paper thumbnail of A State Sum Link Invariant of Regular Isotopy" 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/126243983/A_State_Sum_Link_Invariant_of_Regular_Isotopy">A State Sum Link Invariant of Regular Isotopy</a></div><div class="wp-workCard_item"><span>arXiv (Cornell University)</span><span>, Oct 14, 2007</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT This paper has been withdrawn because there is a fundamental error in the computations; ...</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">ABSTRACT This paper has been withdrawn because there is a fundamental error in the computations; with the right computational scheme it seems to be just a version of the Jones polynomial Comment: This paper has been withdrawn because there is a fundamental error in the computations; with the right computational scheme it seems to be just a version of the Jones polynomial</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="126243983"><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="126243983"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 126243983; 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