2013/12/31 by Ashwin S. Pande
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cohomology #Combinatorics #Computer science #Dual polyhedron #Duality (order theory) #Homotopy and Cohomology in Algebraic Topology #Magnetic monopole #Manifold (fluid mechanics) #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Sequence (biology) #Stack (abstract data type) #Topology (electrical circuits) #hep-th #math-ph #math.GN #math.GT #math.MP #msc:55R65 #msc:81T30
paper · pdf · doi:10.4310/atmp.2018.v22.n6.a5
published as Advances in Theoretical and Mathematical Physics, vol. 22, Number 6, pp. 1535-1591, (2018) · 44 pages,no figures. Submission version. Uses ipart_v1.cls. Minor changes throughout for readability
arxiv created 2017/02/03 · openalex publication_date 2018/01/01 · arxiv updated 2019/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 \citeBunke1. 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 \citeBunke1 and Mathai and Wu \citeMaWu. 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.