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

TL;DR

This paper develops a periodic version of iterated algebraic K-theory for ku, introduces a twisting by higher gerbes, and establishes a form of topological T-duality for sphere bundles oriented with respect to this theory.

Contribution

It introduces a new periodic form of iterated algebraic K-theory and a T-duality framework for sphere bundles, extending previous theories with higher gerbe twistings.

Findings

Defined a periodic iterated algebraic K-theory for ku

Established topological T-duality for sphere bundles with this theory

Connected higher gerbes to the twisting of cohomology

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.