Topological T-duality, automorphisms and classifying spaces

JOURNAL OF GEOMETRY AND PHYSICS

卷:82

Article

Pande, Ashwin S.

关键词: Topological T-duality;    C*-algebras;    Algebraic Topology;    Noncommutative geometry;   

DOI  :  10.1016/j.geomphys.2014.04.004

来源: Elsevier

【 摘 要 】

We extend the formalism of Topological T-duality to spaces which are the total space of a principal S-1-bundle p : E -> W with an H-flux in H-3 (E, Z) 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 (2005). 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 is an element of H-2(X, Z) and H is an element of H-3(X, Z). We construct a classifying space R-3,R-2 for triples in a manner similar to the work of Bunke and Schick (2005). We characterize R-3,R-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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free