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A non-commutative model for higher twisted K-theory

Pennig, Ulrich 2016. A non-commutative model for higher twisted K-theory. Journal of Topology 9 (1) , pp. 27-50. 10.1112/jtopol/jtv033

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Abstract

We develop an operator algebraic model for twisted K-theory, which includes the most general twistings as a generalized cohomology theory (that is, all those classified by the unit spectrum bgl_1(KU)). Our model is based on strongly self-absorbing C*-algebras. We compare it with the known homotopy-theoretic descriptions in the literature, which either use parametrized stable homotopy theory or ∞-categories. We derive a similar comparison of analytic twisted K-homology with its topological counterpart based on generalized Thom spectra. Our model also works for twisted versions of localizations of the K-theory spectrum, like KU[1/n] or KU_ℚ.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: London Mathematical Society
ISSN: 1753-8416
Date of First Compliant Deposit: 2 December 2016
Last Modified: 12 Mar 2020 17:53
URI: http://orca.cf.ac.uk/id/eprint/89479

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  • A non-commutative model for higher twisted K-theory. (deposited 21 Apr 2016 10:18) [Currently Displayed]

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