University of Toronto's Symplectic Geometry Seminar

Feb. 3 2003, 2pm

Lisa Jeffrey

University of Toronto

Cohomology rings of symplectic reduced spaces: the residue formula and the Tolman-Weitsman theorem

Abstract: Suppose M is a symplectic manifold with a Hamiltonian circle action. The Kirwan map is a surjective ring homomorphism from the equivariant cohomology of M to the ordinary cohomology of the symplectic quotient. Two methods have been devised to characterize the kernel of the Kirwan map: (1) the theorem of Tolman and Weitsman and (2) the residue theorem of Jeffrey and Kirwan. I shall give a direct proof of the equivalence between these methods.