nLab David Gepner

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Selected writings

On equivariant elliptic cohomology in (infinity,1)-topos theory.

• David Gepner, Homotopy topoi and equivariant elliptic cohomology

  PhD thesis, University of Illinois at Urbana-Champaign, 2005. (pdf)

• David Gepner, Lennart Meier, On equivariant topological modular forms, (arXiv:2004.10254)

On ∞-groups of units, Thom spectra and twisted generalized cohomology:

• Matthew Ando, Andrew Blumberg, David Gepner, Michael Hopkins, Charles Rezk, Units of ring spectra and Thom spectra (arXiv:0810.4535)

• Matthew Ando, Andrew Blumberg, David Gepner, Michael Hopkins, Charles Rezk, Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory, Journal of Topology, Volume7, Issue 4, December 2014 (arXiv:1403.4320, arXiv:10.1112/jtopol/jtu009)

• Matthew Ando, Andrew Blumberg, David Gepner, Michael Hopkins, Charles Rezk, An $\infty$-categorical approach to $R$-line bundles, $R$-module Thom spectra, and twisted $R$-homology, Journal of Topology Volume 7, Issue 3 2014 Pages 869–893 (arXiv:1403.4325, doi:10.1112/jtopol/jtt035)

Specifically on twisted K-theory and twisted tmf:

• Matthew Ando, Andrew Blumberg, David Gepner, Twists of K-theory and TMF, in Robert S. Doran, Greg Friedman, Jonathan Rosenberg, Superstrings, Geometry, Topology, and $C^*$-algebras, Proceedings of Symposia in Pure Mathematics 81, American Mathematical Society 2010 (arXiv:1002.3004, ISBN:978-0-8218-4887-6)

• Benjamin Antieau, David Gepner, José Manuel Gómez: Actions of Eilenberg-MacLane spaces on K-theory spectra and uniqueness of twisted K-theory, Transactions of the American Mathematical Society 366 7 (2014) 3631–3648 [arXiv:1106.5099 math.KT, doi:10.1090/S0002-9947-2014-05937-0, jstor:23813876]

On Becker-Gottlieb transfer and differential algebraic K-theory:

• Ulrich Bunke, David Gepner, Differential function spectra, the differential Becker-Gottlieb transfer, and applications to differential algebraic K-theory, Memoirs of the American Mathematical Society 2021 (arXiv:1306.0247, ISBN:978-1-4704-4685-7)

On noncommutative motives in terms of algebraic K-theory:

• Andrew Blumberg, David Gepner, Gonçalo Tabuada, A universal characterization of higher algebraic K-theory, Geometry and Topology 17 (2013) 733–838 (arXiv:1001.2282)

On higher algebra in stable $(\infty,1)$-categories:

• David Gepner: An Introduction to Higher Categorical Algebra, chapter in: Handbook of Homotopy Theory, CRC Press (2019) [arXiv:1907.02904, doi:10.1201/9781351251624-13]

On $(\infty,\infty)$-category theory in the generality of lax Gray enrichment:

• David Gepner, Hadrian Heine: Oriented Category Theory (2025) [arXiv:2510.10504]

• David Gepner, Hadrian Heine: Homotopy Posets, Postnikov Towers,and Hypercompletions of $\infty$-Categories [arXiv:2603.09903]

• David Gepner, Hadrian Heine: An Oriented Street–Roberts Conjecture [arXiv:2606.29373]

• David Gepner, Hadrian Heine: Colimits in Oriented Category Theory [arXiv:2608.02592]

Related entries

• noncommutative motive, algebraic K-theory

• (infinity,1)-module bundle, twisted Umkehr map

category: people