Topological Tduality for torus bundles with monodromy
Abstract
We give a simplified definition of topological Tduality that applies to arbitrary torus bundles. The new definition does not involve Chern classes or spectral sequences, only gerbes and morphisms between them. All the familiar topological conditions for Tduals are shown to follow. We determine necessary and sufficient conditions for existence of a Tdual in the case of affine torus bundles. This is general enough to include all principal torus bundles as well as torus bundles with arbitrary monodromy representations. We show that isomorphisms in twisted cohomology, twisted Ktheory and of Courant algebroids persist in this general setting. We also give an example where twisted Ktheory groups can be computed by iterating Tduality.
 Publication:

arXiv eprints
 Pub Date:
 January 2012
 arXiv:
 arXiv:1201.1731
 Bibcode:
 2012arXiv1201.1731B
 Keywords:

 Mathematics  Differential Geometry;
 Mathematical Physics;
 53C08;
 19L50;
 53D18;
 53C80
 EPrint:
 49 pages