Cohomology of a Hamiltonian T-space with involution

Semyon Alesker, Maxim Braverman

Research output: Contribution to journalArticlepeer-review


Let M be a compact symplectic manifold endowed with a Hamiltonian action of a compact torus T with a moment map μ. Suppose there exists a symplectic involution θ : M → M, such that μ ◦ θ = −μ. Assuming that 0 is a regular value of μ, we calculate the character of the action of θ on the cohomology of M in terms of the trace of the action of θ on the symplectic reduction μ−1(0)/T of M. This result generalizes a theorem of R. Stanley, who considered the case when M was a toric variety and dim T = ½ dimM.

Original languageEnglish
Pages (from-to)325-340
Number of pages16
JournalJournal of Symplectic Geometry
Issue number1
StatePublished - 2016

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


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