Topological T-duality for Stacks using a Gysin Sequence
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Publication:6247066
DOI10.4310/ATMP.2018.V22.N6.A5arXiv1312.1791MaRDI QIDQ6247066
Publication date: 6 December 2013
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 -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.
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