Twisted iterated algebraic K-theory and topological T-duality for sphere bundles

Abstract

We introduce a periodic form of the iterated algebraic K-theory of ku, the (connective) complex K-theory spectrum, as well as a natural twisting of this cohomology theory by higher gerbes. Furthermore, we prove a form of topological T-duality for sphere bundles oriented with respect to this theory.

45 pages. Update includes rationality results for spectra admitting a T-duality isomorphism, and extended comments on higher categorical aspects of iterated K-theory. Title changed from "A higher categorical analogue of topological T-duality for sphere bundles." To appear in Annals of K-theory

References in corpus (6)

• Enriched $\infty$-categories via non-symmetric $\infty$-operads
• An $\infty$-categorical approach to $R$-line bundles, $R$-module Thom spectra, and twisted $R$-homology
• Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory
• A Higher Twist in String Theory
• Spherical T-Duality
• Spherical T-duality II: An infinity of spherical T-duals for non-principal SU(2)-bundles

Cited by in corpus (5)

• Twistorial Cohomotopy implies Green-Schwarz anomaly cancellation
• Bordism for the 2-group symmetries of the heterotic and CHL strings
• The Smith Fiber Sequence and Invertible Field Theories
• On the Chern character in Higher Twisted K-theory and spherical T-duality
• A universal characterization of noncommutative motives and secondary algebraic K-theory