Topological T-duality for stacks using a Gysin sequence

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.