Pure and Applied Mathematics Quarterly
Volume 10 (2014)
Topological T-duality for general circle bundles
Pages: 367 – 438
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.
T-duality, twisted $K$-theory, Courant algebroids
2010 Mathematics Subject Classification
Primary 19L50. Secondary 53D18, 55N25.