A noncommutative model for higher twisted K-Theory

Abstract

We develop a operator algebraic model for twisted $K$-theory, which includes the most general twistings as a generalized cohomology theory (i.e. all those classified by the unit spectrum $bg{l}_1(KU)$). Our model is based on strongly self-absorbing $C^{\ast }$-algebras. We compare it with the known homotopy theoretic descriptions in the literature, which either use parametrized stable homotopy theory or $\infty$-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 $K{U}_{\mathbb{Q}}$.

28 pages

References in corpus (1)

• An $\infty$-categorical approach to $R$-line bundles, $R$-module Thom spectra, and twisted $R$-homology

Cited by in corpus (6)

• The character map in (twisted differential) non-abelian cohomology
• Homotopical and operator algebraic twisted K-theory
• Spherical T-Duality and the spherical Fourier-Mukai transform
• Exponential Functors, R-Matrices and Twists
• On the Chern character in Higher Twisted K-theory and spherical T-duality
• Bundles of strongly self-absorbing $C^{\ast }$-algebras with a Clifford grading