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\(T\)-duality for principal torus bundles and dimensionally reduced Gysin sequences. (English) Zbl 1129.53013

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

MSC:

53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
55N20 Generalized (extraordinary) homology and cohomology theories in algebraic topology
55R20 Spectral sequences and homology of fiber spaces in algebraic topology
58B34 Noncommutative geometry (à la Connes)
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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