Topological T-duality is a transformation taking a gerbe on a principal torus
bundle to a gerbe on a principal dual-torus bundle. We give a new geometric
construction of T-dualization, which allows the duality to be extended in
following two directions. First, bundles of groups other than tori, even
bundles of some nonabelian groups, can be dualized. Second, bundles whose duals
are families of noncommutative groups (in the sense of noncommutative geometry)
can be treated, though in this case the base space of the bundles is best
viewed as a topological stack.
Some methods developed for the construction may be of independent interest.
These are a Pontryagin type duality that interchanges commutative principal
bundles with gerbes, a nonabelian Takai type duality for groupoids, and the
computation of certain equivariant Brauer groups.Comment: Same theorems, typos correcte
