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# Pure and Applied Mathematics Quarterly

## Volume 10 (2014)

### Number 3

### Topological T-duality for general circle bundles

Pages: 367 – 438

DOI: http://dx.doi.org/10.4310/PAMQ.2014.v10.n3.a1

#### Author

#### 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.

#### Keywords

T-duality, twisted $K$-theory, Courant algebroids

#### 2010 Mathematics Subject Classification

Primary 19L50. Secondary 53D18, 55N25.