Transformation Groups

, Volume 17, Issue 3, pp 717–746 | Cite as

Equivariant cohomology for Hamiltonian torus actions on symplectic orbifolds

Article

Abstract

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 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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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsCornell UniversityIthacaUSA
  2. 2.Department of Mathematical SciencesASARC, KAISTDaejeonSouth Korea

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