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The topology of T-duality for \(T^{n}\)-bundles. (English) Zbl 1116.55007

\(T\)-duality is a relation between two string theories on the level of quantum field theories. The authors of the present paper are interested in giving a precise mathematical characterization of \(T\)-duality for topological spaces. They define for any Hausdorff and paracompact topological space \(B\) a pair, \((F,h)\), over \(B\) as a principal \(T^n\)-bundle \(F\to B\), where \(T^n=U(1)\times\cdots_n\cdots U(1)\) is the \(n\)-dimensional torus, and \(h\in H^3(F;{\mathbb Z})\) such that it represents a cohomology class of twists over \(F\), by means of the isomorphism \(\left\{\text{ category of twists over }F\)

MSC:

55R15 Classification of fiber spaces or bundles in algebraic topology
55T10 Serre spectral sequences
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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