Topological T-duality, Automorphisms and Classifying Spaces
Ashwin S. Pande

TL;DR
This paper extends topological T-duality to principal circle bundles with H-flux, connecting it to automorphisms of continuous-trace algebras and classifying spaces, revealing a topological framework for T-duality transformations.
Contribution
It introduces a topological approach to T-duality involving automorphisms of continuous-trace algebras and constructs a classifying space for T-duality triples, advancing the mathematical understanding of the duality.
Findings
Constructed a classifying space R_{3,2} for T-duality triples.
Established a natural self-map on R_{3,2} inducing T-duality.
Connected topological T-duality to automorphisms of continuous-trace algebras.
Abstract
We extend the formalism of Topological T-duality to spaces which are the total space of a principal -bundle with an -flux in together the together with an automorphism of the continuous-trace algebra on determined by . The automorphism is a `topological approximation' to a gerby gauge transformation of spacetime. We motivate this physically from Buscher's Rules for T-duality. Using the Equivariant Brauer Group, we connect this problem to the -algebraic formalism of Topological T-duality of Mathai and Rosenberg. We show that the study of this problem leads to the study of a purely topological problem, namely, Topological T-duality of triples consisting of isomorphism classes of a principal circle bundle and classes and We construct a classifying space for triples in a…
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