nLab
Charles Rezk

website

Selected writings

On the homotopy theory of homotopy theories (the (infinity,1)-category of (infinity,1)-categories) in terms of complete Segal spaces:

Charles Rezk, A model for the homotopy theory of homotopy theory, Trans. Amer. Math. Soc. 353 (2001), 973-1007 (arXiv:math/9811037, doi:10.1090/S0002-9947-00-02653-2)

Introducing model toposes/(∞,1)-toposes:

Charles Rezk, Toposes and homotopy toposes, 2010 (pdf)

Review of higher topos theory:

Charles Rezk, Lectures on Higher Topos Theory, Leeds 2019 (pdf, pdf)

On complete Segal spaces:

Charles Rezk, A model for the homotopy theory of homotopy theory , Trans. Amer. Math. Soc., 353(3), 973-1007 (pdf)

On power operations:

Charles Rezk, Lectures on power operations (dvi) (2006)
Charles Rezk, Power operations in Morava E-theory – a survey (2009) (pdf)
Charles Rezk, Isogenies, power operations, and homotopy theory, article (pdf) and talk at ICM 2014 (pdf)

Expressing logarithmic cohomology operations in terms of the Bousfield-Kuhn functor and power operations:

Charles Rezk, The units of a ring spectrum and a logarithmic cohomology operation, J. Amer. Math. Soc. 19 (2006), 969-1014 (arXiv:math/0407022)

On the string orientation of tmf:

Matthew Ando, Michael Hopkins, Charles Rezk, Multiplicative orientations of KO-theory and the spectrum of topological modular forms, 2010 (pdf)

On global equivariant homotopy theory as a cohesive (∞,1)-topos:

Charles Rezk, Global Homotopy Theory and Cohesion, 2014
(pdf, pdf)

On sufficient conditions for geometric realization of simplicial topological spaces to commute with homotopy pullback

Charles Rezk, When are homotopy colimits compatible with homotopy base change?, 2014 (pdf, pdf)

On Theta-spaces:

Charles Rezk, A cartesian presentation of weak $n$ -categories Geom. Topol. 14 (2010), no. 1, 521–571 (arXiv:0901.3602)

Correction to “A cartesian presentation of weak $n$ -categories” Geom. Topol. 14 (2010), no. 4, 2301–2304. MR 2740648 (pdf)

Charles Rezk, Cartesian presentations of weak n-categories
An introduction to $\Theta_n$ -spaces_ (2009) (pdf)

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)

Related $n$ Lab entries

in higher algebra/stable homotopy theory

in higher category theory:

in higher topos theory:

category: people

Last revised on September 4, 2020 at 14:33:43. See the history of this page for a list of all contributions to it.