Cohomology of a Hamiltonian T -space with Involution
نویسنده
چکیده
Let M be a compact symplectic manifold on which a compact torus T acts Hamiltonialy 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 character of the action of θ on the symplectic reduction μ(0)/T of M . This result generalizes a theorem of R. Stanley, who considered the case when M was a toric variety and dimT = 1 2 dimR M .
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