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Equivariant cohomology for Hamiltonian torus actions on symplectic orbifolds

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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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Authors and Affiliations

  1. Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA

    T. S. Holm

  2. Department of Mathematical Sciences, ASARC, KAIST, Daejeon, South Korea

    T. Matsumura

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  1. T. S. Holm
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  2. T. Matsumura
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Correspondence to T. S. Holm.

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Holm, T.S., Matsumura, T. Equivariant cohomology for Hamiltonian torus actions on symplectic orbifolds. Transformation Groups 17, 717–746 (2012). https://doi.org/10.1007/s00031-012-9192-7

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