# University of Toronto's Symplectic Geometry Seminar

Feb. 3 2003, 2pm

SS5017A

## 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.