  We present an explicit formula for the topology and H-flux of the T-dual of a
general type II compactification, significantly generalizing earlier results.
Our results apply to T-dualities with respect to any circle action on
spacetime. As before, T-duality exchanges type IIA and type IIB string
theories. A new consequence is that the T-dual spacetime is a singular space
when the fixed point set is non-empty; the singularities correspond to
Kaluza-Klein monopoles. We propose that the Ramond-Ramond charges of type II
string theories on the singular dual are classified by twisted equivariant
cohomology groups. We also include the K-theory approach.
