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

John A. Lind; Hisham Sati; Craig Westerland

doi:10.2140/akt.2020.5.1

Abstract

We introduce a periodic form of the iterated algebraic $K$ -theory of $k u$ , 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.

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John A. Lind. Hisham Sati. Craig Westerland. "Twisted iterated algebraic $K$-theory and topological T-duality for sphere bundles." Ann. K-Theory 5 (1) 1 - 42, 2020. https://doi.org/10.2140/akt.2020.5.1

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Received: 8 December 2017; Revised: 12 August 2019; Accepted: 28 August 2019; Published: 2020

First available in Project Euclid: 11 August 2020

zbMATH: 07181993

MathSciNet: MR4078224

Digital Object Identifier: 10.2140/akt.2020.5.1

Subjects:

Primary: 19D99 , 55N20 , 55R15 , 55R65

Secondary: 18D05 , 19L50 , 55P43

Keywords: $n$-gerbes , iterated algebraic $K$-theory , T-duality , twisted $K$-theory

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