Topological T-duality for general circle bundles

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.