Homotopical and operator algebraic twisted K-theory

Abstract

Using the framework for multiplicative parametrized homotopy theory introduced in joint work with C. Schlichtkrull, we produce a multiplicative comparison between the homotopical and operator algebraic constructions of twisted K-theory, both in the real and complex case. We also improve several comparison results about twisted K-theory of C*-algebras to include multiplicative structures. Our results can also be interpreted in the infinity-categorical setup for parametrized spectra.

v3: 32 pages, minor revision. Accepted for publication in Mathematische Annalen

References in corpus (4)

• Global homotopy theory
• An $\infty$-categorical approach to $R$-line bundles, $R$-module Thom spectra, and twisted $R$-homology
• Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces
• Generalized Thom spectra and their topological Hochschild homology

Cited by in corpus (4)

• Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces
• Bosonization and Anomaly Indicators of (2+1)-D Fermionic Topological Orders
• Bundles of strongly self-absorbing $C^{\ast }$-algebras with a Clifford grading
• Line Bundle Twists for Unitary Bordism are Ghosts