Cohomology of a Hamiltonian T-space with involution

Abstract

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 trace of the action of $\theta$ on the cohomology of $M$ in terms of the trace 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.

A new proof based on application of the equivariant Kirwan-Morse inequalities is given

References in corpus (2)

• On Generalized $h$--Vectors of Rational Polytopes with a Symmetry of Prime Order
• Novikov inequalities with symmetry

Cited by in corpus (1)

• Kirwan-Novikov inequalities on a manifold with boundary