Cohomology of a Hamiltonian T-space with involution

Details Cohomology of a Hamiltonian T-space with involution Cohomology of a Hamiltonian T-space with involution

1999-04-26

arxiv.org/abs/math/9904148v2

Mathematics

Symplectic Geometry

LaTeX 2e, 10 pages, minor misprints were corrected

Scientific paper

Let $M$ be a compact symplectic manifold on which a compact torus $T$ acts Hamiltonialy with a moment map $\mu$. Suppose there exists a symplectic involution $\theta:M\to M$, such that $\mu\circ\theta=-\mu$. Assuming that 0 is a regular value of $\mu$, we calculate the character of the action of $\theta$ on the cohomology of $M$ in terms of the character of the action of $\theta$ on the symplectic reduction $\mu^{-1}(0)/T$ of $M$. This result generalizes a theorem of R. Stanley, who considered the case when $M$ was a toric variety.

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