INTERSECTION COHOMOLOGY OF SYMPLECTIC QUOTIENTS BY CIRCLE ACTIONS

Let T = U(1) and M be a Hamiltonian T-space with proper moment map μ :M −→ R. When 0 is not a regular value of μ, the symplectic quotient X = μ−1(0)/T is a singular stratified space. A description is provided of the middle perversity intersection cohomology of X as a subspace of the equivariant cohomology H∗ T (μ−1(0)). The approach is sheaf theoretic.