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# Advances in Theoretical and Mathematical Physics

## Volume 22 (2018)

### Number 6

### Topological T-duality for stacks using a Gysin sequence

Pages: 1535 – 1591

DOI: http://dx.doi.org/10.4310/ATMP.2018.v22.n6.a5

#### Author

#### Abstract

In this paper we study the topological T-dual of spaces with a non-free circle action mainly using the stack theory method of Bunke and co-workers. We first compare three formalisms for obtaining the Topological T-dual of a semi-free S1-space in a simple example. Then, we calculate the T-dual of general KK-monopole backgrounds using the stack theory method. We define the dyonic coordinate for these backgrounds. We introduce an approach to Topological T-duality using classifying spaces which simultaneously generalizes the methods of Bunke et al and Mathai and Wu. Then, we define a cohomology Gysin sequence for prinicpal bundles of stacks and describe an application to Topological T-duality for stacks. We apply the above to calculate the Topological T-dual of a general compact three-manifold with an arbitrary smooth circle action. We point out a possible application of these T-duals to higher-dimensional black holes.

Published 3 May 2019