A Cech Dimensionally Reduced Gysin Sequence for Principal Torus Bundles

TL;DR

This paper develops a Cech cohomology-based Gysin sequence for principal torus bundles, extending previous de Rham cohomology models to better understand T-duality with NS H-Flux.

Contribution

It introduces a new Cech cohomology framework that forms a Gysin sequence for principal torus bundles, complementing existing de Rham models.

Findings

Constructed Cech cohomology groups forming a Gysin sequence

Extended the understanding of T-duality with NS H-Flux

Provided a new computational tool for global properties of torus bundles

Abstract

In this paper we construct Cech cohomology groups that form a Gysin-type long exact sequence for principal torus bundles. This sequence is modeled on a de Rham cohomology sequence published in earlier work by Bouwknegt, Hannabuss and Mathai, which was developed to compute the global properties of T-duality in the presence of NS H-Flux.