Vol. 5, No. 1, 2020

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

John A. Lind, Hisham Sati and Craig Westerland

Vol. 5 (2020), No. 1, 1–42
DOI: 10.2140/akt.2020.5.1
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.

Keywords
T-duality, iterated algebraic $K$-theory, twisted $K$-theory, $n$-gerbes
Mathematical Subject Classification 2010
Primary: 19D99, 55N20, 55R15, 55R65
Secondary: 18D05, 19L50, 55P43
Milestones
Received: 8 December 2017
Revised: 12 August 2019
Accepted: 28 August 2019
Published: 21 March 2020
Authors
John A. Lind
Department of Mathematics and Statistics
California State University, Chico
Chico, CA
United States
Hisham Sati
Department of Mathematics
New York University Abu Dhabi
Saadiyat Island
Abu Dhabi
United Arab Emirates
Craig Westerland
School of Mathematics
University of Minnesota
Minneapolis, MN
United States