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Topological T-duality for general circle bundles

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arxiv 1105.0290 v3 pith:7ICE5YJD submitted 2011-05-02 math.DG math.KT

David Baraglia This is my paper · ORCID
classification math.DGmath.KT
keywords bundlescircletheorytwistedcohomologygeneralt-dualt-duality
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abstract

We extend topological T-duality to the case of general circle bundles. In this setting we prove existence and uniqueness of T-duals. We then show that T-dual spaces have isomorphic twisted cohomology, twisted $K$-theory and Courant algebroids. A novel feature is that we must consider two kinds of twists in de Rham cohomology and $K$-theory, namely by degree 3 integral classes and a less familiar kind of twist using real line bundles. We give some examples of T-dual non-oriented circle bundles and calculate their twisted $K$-theory.

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  1. Courant Algebroid Relations, T-Dualities and Generalised Ricci Flow

    hep-th 2025-02 conditional novelty 6.0 of 10

    Using Courant algebroid relations, the authors prove that geometric T-duality maps solutions of generalized Ricci flow to solutions of generalized Ricci flow, preserving the generalized string background equations.

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