T-duality for principal torus bundles and dimensionally reduced Gysin sequences

We reexamine the effects of T-duality on the global properties for principal circle bundles in the context of a dimensionally reduced Gysin sequence. We then construct a Gysin sequence for principal torus bundles and examine the consequences. In particular, we argue that the T-dual of a principal torus bundle with nontrivial H-flux is, in general, a continuous field of noncommutative, nonassociative tori.

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Published 1 January 2005