Equivariant cohomology for Hamiltonian torus actions on symplectic orbifolds

Details Equivariant cohomology for Hamiltonian torus actions on symplectic orbifolds Equivariant cohomology for Hamiltonian torus actions on symplectic orbifolds

2010-08-19

arxiv.org/abs/1008.3315v1

Mathematics

Symplectic Geometry

29 pages

Scientific paper

In this paper, we study Hamiltonian R-actions on symplectic orbifolds [M/S], where R and S are tori. We prove an injectivity theorem and generalize Tolman-Weitsman's proof of the GKM theorem in this setting. The main example is the symplectic reduction X//S of a Hamiltonian T-manifold X by a subtorus S of T. This includes the class of symplectic toric orbifolds. We define the equivariant Chen-Ruan cohomology ring and use the above results to establish a combinatorial method of computing this equivariant Chen-Ruan cohomology in terms of orbifold fixed point data.

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