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T-duality, in its simplest form, is the R to 1/R symmetry of
String Theory compactified on a circle of radius R. It can be
generalized to manifolds which admit circle actions (e.g. circle
bundles) or, more generally, torus actions. In the case of nontrivial
circle bundles, and in the background of H-flux, T-duality relates
manifolds of different topology and in particular provides
isomorphisms between the twisted cohomologies and twisted K-theories
of these manifolds. In this talk we will discuss these developments
as well as provide some examples. We will also discuss the
obstruction to T-dualizing higher dimensional torii in the background
of H-flux.
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