A new approach to topological T-duality for principal torus bundles

TL;DR

This paper presents a new Thom class-based formulation of topological T-duality for principal torus bundles, simplifying proofs and removing previous global assumptions on H-flux, thus advancing the mathematical understanding of T-duality.

Contribution

It introduces a Thom class approach to topological T-duality that simplifies existing proofs and generalizes local formulations to torus bundles.

Findings

Equivalent to previous definitions but with fewer assumptions

Simplifies classification proofs of T-duals

Extends local T-duality formulations to higher-dimensional torus bundles

Abstract

We introduce a new `Thom class' formulation of topological T-duality for principal torus bundles. This definition is equivalent to the established one of Bunke, Rumpf, and Schick but has the virtue of removing the global assumptions on the H-flux required in the old definition. With the new definition, we provide easier and more transparent proofs of the classification of T-duals and generalise the local formulation of T-duality for circle bundles by Bunke, Schick, and Spitzweck to the torus case.