2012/11/30 by Ashwin S. Pande · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Automorphism #Combinatorics #Homotopy #Homotopy and Cohomology in Algebraic Topology #Isomorphism (crystallography) #Mathematics #Pure mathematics #Topology (electrical circuits) #hep-th #math-ph #math.AT #math.MP #msc:55-XX #msc:81T30 #msc:83E30
paper · pdf · doi:10.1016/j.geomphys.2014.04.004
published as Journal of Geometry and Physics, {\bf 82}, pp. 98-123, (2014) · 38 pages, no figures, extensive revisions to Sec. (1) and (2)
arxiv created 2013/10/02 · openalex publication_date 2014/04/18 · arxiv updated 2014/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We extend the formalism of Topological T-duality to spaces which are the total space of a principal S1-bundle p:E → W with an H-flux in H3(E,Z) together the together with an automorphism of the continuous-trace algebra on E determined by H. 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 C∗-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 (p,b,H) consisting of isomorphism classes of a principal circle bundle p:X → B and classes b ∈ H2(X,Z) and H ∈ H3(X,Z). We construct a classifying space R3,2 for triples in a manner similar to the work of Bunke and Schick \citeBunke. We characterize R3,2 up to homotopy and study some of its properties. We show that it possesses a natural self-map which induces T-duality for triples. We study some properties of this map.