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We study Hamiltonian R-actions on symplectic orbifolds [M/S], where R and S are tori. We prove an injectivity theorem and generalize Tolman and Weitsman’s proof of the GKM theorem [TW] in this setting. The main example is the symplectic reduction X//S of a Hamiltonian T-manifold X by a subtorus S ⊂ T. This includes the class of symplectic toric orbifolds. We define the equivariant Chen–Ruan cohomology...
Let X be a topological space upon which a compact connected Lie group G acts. It is well known that the equivariant cohomology H*G (X; Q) is isomorphic to the subalgebra of Weyl group invariants of the equivariant cohomology H*T (X; Q), where T is a maximal torus of G. This relationship breaks down for coefficient rings k other than Q. Instead, we prove that under a mild condition on k the...
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