Topological T-duality, automorphisms and classifying spaces

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 (2005). 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.