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width: 0.3em;"></span> <a href="/nlab/show/diff/HomePage" accesskey="H" title="Home page">Home Page</a> | <a href="/nlab/all_pages" accesskey="A" title="List of all pages">All Pages</a> | <a href="/nlab/latest_revisions" accesskey="U" title="Latest edits and page creations">Latest Revisions</a> | <a href="https://nforum.ncatlab.org/discussion/16160/#Item_1" title="Discuss this page in its dedicated thread on the nForum" style="color: black">Discuss this page</a> | <form accept-charset="utf-8" action="/nlab/search" id="navigationSearchForm" method="get"> <fieldset class="search"><input type="text" id="searchField" name="query" value="Search" style="display:inline-block; float: left;" onfocus="this.value == 'Search' ? this.value = '' : true" onblur="this.value == '' ? this.value = 'Search' : true" /></fieldset> </form> <span id='navEnd'></span> </div> <div id="revision"> <p class="show_diff"> Showing changes from revision #13 to #14: <ins class="diffins">Added</ins> | <del class="diffdel">Removed</del> | <del class="diffmod">Chan</del><ins class="diffmod">ged</ins> </p> <ul> <li><a href='http://www.mathematik.uni-regensburg.de/Bunke/'>website</a></li> </ul> <h2 id='selected_writings'>Selected writings</h2> <p>On <a class='existingWikiWord' href='/nlab/show/diff/topological+T-duality'>topological T-duality</a>:</p> <ul> <li id='BunkeSchick04'> <p><a class='existingWikiWord' href='/nlab/show/diff/Ulrich+Bunke'>Ulrich Bunke</a>, <a class='existingWikiWord' href='/nlab/show/diff/Thomas+Schick'>Thomas Schick</a>, <em>On the topology of T-duality</em>, Rev. Math. Phys. <strong>17</strong> (2005) 77-112 [[arXiv:math/0405132](https://arxiv.org/abs/math/0405132), <a href='https://doi.org/10.1142/S0129055X05002315'>doi:10.1142/S0129055X05002315</a>]</p> </li> <li id='BunkeRumpfSchick08'> <p id='BunkeRumpfSchick08'> <a class='existingWikiWord' href='/nlab/show/diff/Ulrich+Bunke'>Ulrich Bunke</a>, P. Rumpf, <a class='existingWikiWord' href='/nlab/show/diff/Thomas+Schick'>Thomas Schick</a>, <em>The topology of <math class='maruku-mathml' display='inline' id='mathml_2fcdca53b9cad1d876441c8e0e6e1a2e0d48ce17_1' xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow><mi>T</mi></mrow><annotation encoding='application/x-tex'>T</annotation></semantics></math>-duality for <math class='maruku-mathml' display='inline' id='mathml_2fcdca53b9cad1d876441c8e0e6e1a2e0d48ce17_2' xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow><msup><mi>T</mi> <mi>n</mi></msup></mrow><annotation encoding='application/x-tex'>T^n</annotation></semantics></math>-bundles</em>, Rev. Math. Phys. <strong>18</strong> 1103 (2006) [[arXiv:math.GT/0501487](http://arxiv.org/abs/math.GT/0501487), <a href='https://doi.org/10.1142/S0129055X06002875'>doi:10.1142/S0129055X06002875</a>]</p> </li> </ul> <p>On <a class='existingWikiWord' href='/nlab/show/diff/twisted+ad-equivariant+K-theory'>twisted ad-equivariant K-theory</a> via <a class='existingWikiWord' href='/nlab/show/diff/differentiable+stack'>differentiable stacks</a>:</p> <ul> <li><a class='existingWikiWord' href='/nlab/show/diff/Ulrich+Bunke'>Ulrich Bunke</a>, Ingo Schroeder, <em>Twisted K-Theory and TQFT</em> (<a href='https://arxiv.org/abs/math/0504458'>arXiv:math/0504458</a>, <a href='https://inspirehep.net/literature/681555'>spire:681555</a>)</li> </ul> <p>On <a class='existingWikiWord' href='/nlab/show/diff/differential+cohomology'>differential cohomology</a>:</p> <ul> <li><a class='existingWikiWord' href='/nlab/show/diff/Ulrich+Bunke'>Ulrich Bunke</a>, <em>Differential cohomology</em> (<a href='http://arxiv.org/abs/1208.3961'>arXiv:1208.3961</a>)</li> </ul> <p>On <a class='existingWikiWord' href='/nlab/show/diff/differential+K-theory'>differential K-theory</a>:</p> <ul> <li id='BunkeSchickReferences'><a class='existingWikiWord' href='/nlab/show/diff/Ulrich+Bunke'>Ulrich Bunke</a>, <a class='existingWikiWord' href='/nlab/show/diff/Thomas+Schick'>Thomas Schick</a>, <em>Smooth K-Theory</em>, Astérisque 328 (2009), 45-135 (<a href='http://arxiv.org/abs/0707.0046'>arXiv:0707.0046</a>, <a href='http://www.numdam.org/item/?id=AST_2009__328__45_0'>numdam:AST_2009__328__45_0</a>)</li> </ul> <p>On <a class='existingWikiWord' href='/nlab/show/diff/differential+cohomology'>differential cohomology</a> and the <a class='existingWikiWord' href='/nlab/show/diff/Adams+e-invariant'>e-invariant</a>:</p> <ul> <li><a class='existingWikiWord' href='/nlab/show/diff/Ulrich+Bunke'>Ulrich Bunke</a>, Section 2 of: <em>Differential cohomology in geometry and analysis</em>, talk 2008 (<a href='https://www.uni-regensburg.de/Fakultaeten/nat_Fak_I/Bunke/Vortrag-Erlangen.pdf'>pdf</a>, <a class='existingWikiWord' href='/nlab/files/BunkeEInvariantErlangen2008.pdf' title='pdf'>pdf</a>)</li> </ul> <p>On <a class='existingWikiWord' href='/nlab/show/diff/differential+cobordism+cohomology'>differential cobordism cohomology</a>, i.e. enhancement of <a class='existingWikiWord' href='/nlab/show/diff/MU'>MU</a> (<a class='existingWikiWord' href='/nlab/show/diff/MU'>complex cobordism cohomology</a>) to <a class='existingWikiWord' href='/nlab/show/diff/differential+cohomology'>differential cohomology</a>:</p> <ul> <li><a class='existingWikiWord' href='/nlab/show/diff/Ulrich+Bunke'>Ulrich Bunke</a>, <a class='existingWikiWord' href='/nlab/show/diff/Thomas+Schick'>Thomas Schick</a>, Ingo Schroeder, Moritz Wiethaup, <em>Landweber exact formal group laws and smooth cohomology theories</em>, Algebr. Geom. Topol. <strong>9</strong> (2009) 1751-1790 [[arXiv:0711.1134](https://arxiv.org/abs/0711.1134), <a href='https://doi.org/10.2140/agt.2009.9.1751'>doi:10.2140/agt.2009.9.1751</a>]</li> </ul> <p>On the <a class='existingWikiWord' href='/nlab/show/diff/differential+cohomology+diagram'>differential cohomology hexagon</a>:</p> <ul> <li id='BunkeNikolausVoelkl13'><a class='existingWikiWord' href='/nlab/show/diff/Ulrich+Bunke'>Ulrich Bunke</a>, <a class='existingWikiWord' href='/nlab/show/diff/Thomas+Nikolaus'>Thomas Nikolaus</a>, <a class='existingWikiWord' href='/nlab/show/diff/Michael+V%C3%B6lkl'>Michael Völkl</a>, <em>Differential cohomology theories as sheaves of spectra</em>, Journal of Homotopy and Related Structures October 2014 (<a href='http://arxiv.org/abs/1311.3188'>arXiv:1311.3188</a>)</li> </ul> <p>On <a class='existingWikiWord' href='/nlab/show/diff/secondary+characteristic+class'>secondary characteristic classes</a> in <a class='existingWikiWord' href='/nlab/show/diff/String+bordism'>string cobordism cohomology theory</a> and in <a class='existingWikiWord' href='/nlab/show/diff/tmf'>tmf</a>:</p> <ul> <li><a class='existingWikiWord' href='/nlab/show/diff/Ulrich+Bunke'>Ulrich Bunke</a>, <a class='existingWikiWord' href='/nlab/show/diff/Niko+Naumann'>Niko Naumann</a>, <em>Secondary Invariants for String Bordism and tmf</em>, Bulletin des Sciences Mathématiques <strong>138</strong>:8 (2014) 912–970 (<a href='https://doi.org/10.1016/j.bulsci.2014.05.002'>doi:10.1016/j.bulsci.2014.05.002</a>)</li> </ul> <p>Introducing <a class='existingWikiWord' href='/nlab/show/diff/differential+algebraic+K-theory'>differential algebraic K-theory</a> with application to <a class='existingWikiWord' href='/nlab/show/diff/higher+regulator'>higher</a> <a class='existingWikiWord' href='/nlab/show/diff/higher+regulator'>Beilinson regulators</a>:</p> <ul> <li id='BunkeTamme12'> <p><a class='existingWikiWord' href='/nlab/show/diff/Ulrich+Bunke'>Ulrich Bunke</a>, <a class='existingWikiWord' href='/nlab/show/diff/Georg+Tamme'>Georg Tamme</a>, <em>Regulators and cycle maps in higher-dimensional differential algebraic K-theory</em>, Advances in Mathematics Volume 285, 5 November 2015, Pages 1853-1969 (<a href='http://arxiv.org/abs/1209.6451'>arXiv:1209.6451</a>, <a href='https://doi.org/10.1016/j.aim.2015.08.004'>doi:10.1016/j.aim.2015.08.004</a>)</p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/diff/Ulrich+Bunke'>Ulrich Bunke</a>, <a class='existingWikiWord' href='/nlab/show/diff/David+Gepner'>David Gepner</a>, <em>Differential function spectra, the differential Becker-Gottlieb transfer, and applications to differential algebraic K-theory</em>, Memoirs of the American Mathematical Society 2021 (<a href='httpS://arxiv.org/abs/1306.0247'>arXiv:1306.0247</a>, <a href='https://bookstore.ams.org/cdn-1608276327798/memo-269-1316/'>ISBN:978-1-4704-4685-7</a>)</p> </li> <li id='BunkeTamme13'> <p><a class='existingWikiWord' href='/nlab/show/diff/Ulrich+Bunke'>Ulrich Bunke</a>, <a class='existingWikiWord' href='/nlab/show/diff/Georg+Tamme'>Georg Tamme</a>, <em>Multiplicative differential algebraic K-theory and applications</em>, Ann. K-Theory 1(3): 227–258 (2016) (<a href='http://arxiv.org/abs/1311.1421'>arXiv:1311.1421</a>, <a href='https://doi.org/10.2140/akt.2016.1.227'>doi:10.2140/akt.2016.1.227</a>)</p> </li> </ul> <p>On (<a class='existingWikiWord' href='/nlab/show/diff/equivariant+K-theory'>equivariant</a>) <a class='existingWikiWord' href='/nlab/show/diff/KK-theory'>KK-theory</a> as the <a class='existingWikiWord' href='/nlab/show/diff/homotopy+category+of+an+%28infinity%2C1%29-category'>homotopy category</a> of a <a class='existingWikiWord' href='/nlab/show/diff/stable+%28infinity%2C1%29-category'>stable $(\infty,1)$-category</a>:</p> <ul> <li id='BunkeEngelLand21'><a class='existingWikiWord' href='/nlab/show/diff/Ulrich+Bunke'>Ulrich Bunke</a>, <a class='existingWikiWord' href='/nlab/show/diff/Alexander+Engel'>Alexander Engel</a>, <a class='existingWikiWord' href='/nlab/show/diff/Markus+Land'>Markus Land</a>, <em>A stable <math class='maruku-mathml' display='inline' id='mathml_2fcdca53b9cad1d876441c8e0e6e1a2e0d48ce17_3' xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow><mn>∞</mn></mrow><annotation encoding='application/x-tex'>\infty</annotation></semantics></math>-category for equivariant KK-theory</em> <math class='maruku-mathml' display='inline' id='mathml_2fcdca53b9cad1d876441c8e0e6e1a2e0d48ce17_4' xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow><mo stretchy='false'>[</mo></mrow><annotation encoding='application/x-tex'>[</annotation></semantics></math><a href='https://arxiv.org/abs/2102.13372'>arXiv:2102.13372</a><math class='maruku-mathml' display='inline' id='mathml_2fcdca53b9cad1d876441c8e0e6e1a2e0d48ce17_5' xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow><mo stretchy='false'>]</mo></mrow><annotation encoding='application/x-tex'>]</annotation></semantics></math></li> </ul> <p>On (topological) <a class='existingWikiWord' href='/nlab/show/diff/inertia+orbifold'><span> inertia<del class='diffmod'> stack</del><ins class='diffmod'> stacks</ins></span></a><span><del class='diffmod'> s</del><ins class='diffmod'> :</ins></span></p> <ul> <li><a class='existingWikiWord' href='/nlab/show/diff/Ulrich+Bunke'>Ulrich Bunke</a>, <a class='existingWikiWord' href='/nlab/show/diff/Markus+Spitzweck'>Markus Spitzweck</a>, <a class='existingWikiWord' href='/nlab/show/diff/Thomas+Schick'>Thomas Schick</a>, <em>Inertia and delocalized twisted cohomology</em>, Homotopy, Homology and Applications 10(1) 129–180 (2008) <a href='https://arxiv.org/abs/math/0609576'>math.KT/0609576</a> <br /><a href='https://doi.org/10.4310/HHA.2008.v10.n1.a6'>doi</a></li> </ul><ins class='diffins'> </ins><ins class='diffins'><p>On <a class='existingWikiWord' href='/nlab/show/diff/coarse+topology'>coarse topology</a>:</p></ins><ins class='diffins'> </ins><ins class='diffins'><ul> <li><a class='existingWikiWord' href='/nlab/show/diff/Ulrich+Bunke'>Ulrich Bunke</a>, <em>Coarse geometry</em>, in <em><a class='existingWikiWord' href='/nlab/show/diff/Encyclopedia+of+Mathematical+Physics+2nd+ed'>Encyclopedia of Mathematical Physics 2nd ed</a></em>, Elsevier (2024) [[arXiv:2305.09203](https://arxiv.org/abs/2305.09203)]</li> </ul></ins> <h2 id='related_entries'>Related entries</h2> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/diff/differential+cohomology'>differential cohomology</a></p> <ul> <li><a class='existingWikiWord' href='/nlab/show/diff/differential+K-theory'>differential K-theory</a></li> </ul> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/diff/topological+T-duality'>topological T-duality</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/diff/quantum+anomaly'>quantum anomaly</a></p> </li> </ul> <p><div class='property'> category: <a class='category_link' href='/nlab/list/people'>people</a></div></p> <p> </p> </div> <div class="revisedby"> <p> Last revised on March 26, 2024 at 19:19:25. 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