Equivariant cohomology of K-contact manifolds

Extended Manifolds and Extended Equivariant Cohomology

We define the category of manifolds with extended tangent bundles, we study their symmetries and we consider the analogue of equivariant cohomology for actions of Lie groups in this category. We show that when the action preserves the splitting of the extended tangent bundle, our definition of extended equivariant cohomology agrees with the twisted equivariant de Rham model of Cartan, and for t...

The Equivariant Cohomology Theory of Twisted Generalized Complex Manifolds

It has been shown recently by Kapustin and Tomasiello that the mathematical notion of Hamiltonian actions on twisted generalized Kähler manifolds is in perfect agreement with the physical notion of general (2, 2) gauged sigma models with three-form fluxes. In this article, we study the twisted equivariant cohomology theory of Hamiltonian actions on H-twisted generalized complex manifolds. If th...

The quantum equivariant cohomology of toric manifolds through mirror symmetry

Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten invariants of the target manifold. e-mail address: [email protected] address: Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands

On K-contact Einstein Manifolds

The object of the present paper is to characterize K-contact Einstein manifolds satisfying the curvature condition R · C = Q(S,C), where C is the conformal curvature tensor and R the Riemannian curvature tensor. Next we study K-contact Einstein manifolds satisfying the curvature conditions C ·S = 0 and S ·C = 0, where S is the Ricci tensor. Finally, we consider K-contact Einstein manifolds sati...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology