Communications in Mathematical Physics

, Volume 316, Issue 1, pp 279–286 | Cite as

Topology and Flux of T-Dual Manifolds with Circle Actions

  • Varghese Mathai
  • Siye Wu


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 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 \({X^\mathbb{T}}\) 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.


High Energy Phys Equivariant Cohomology Circle Action Singular Space Intersection Cohomology 
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© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of AdelaideAdelaideAustralia
  2. 2.Department of MathematicsUniversity of Hong KongHong KongChina.

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