Varghese, M.Wu, S.2013-01-032013-01-032012Communications in Mathematical Physics, 2012; 316(1):279-2860010-36161432-0916http://hdl.handle.net/2440/74718We 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 X. 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 XT 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 discuss the K-theory approach.en© Springer-Verlag 2012Quantum PhysicsMathematical PhysicsTheoretical, Mathematical and Computational PhysicsStatistical Physics, Dynamical Systems and ComplexityClassical and Quantum Gravitation, Relativity TheoryJournal article002012285810.1007/s00220-012-1542-80003103422000102-s2.0-8486820422222658Varghese, M. [0000-0002-1100-3595]