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 \cite{Bunke1}. We first compare three formalisms for obtaining the Topological T-dual of a semi-free $S^1$-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 \cite{Bunke1} and Mathai and Wu \cite{MaWu}. 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 {\em arbitrary} smooth circle action. We point out a possible application of these T-duals to higher-dimensional black holes.

44 pages,no figures. Submission version. Uses ipart_v1.cls. Minor changes throughout for readability

References in corpus (6)

• Foundations of Topological Stacks I
• Worldsheet Instanton Corrections to the Kaluza-Klein Monopole
• Topology and Flux of T-Dual Manifolds with Circle Actions
• Group actions on stacks and applications to equivariant string topology for stacks
• Topological T-duality, Automorphisms and Classifying Spaces
• Topological T-duality and Kaluza-Klein Monopoles

Cited by in corpus (1)

• Equivariant Topological T-Duality