Topological T-duality for general circle bundles

Details Topological T-duality for general circle bundles Topological T-duality for general circle bundles

2011-05-02

arxiv.org/abs/1105.0290v3

Mathematics

Differential Geometry

62 pages, Sections 6.5, 7.3 fixed

Scientific paper

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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