University of Toronto's Symplectic Geometry Seminar

April 5, 2004, Monday, 2:10 - 3 PM

Joon-Hyeok Song

U of Toronto

Intersection numbers in reduced spaces of quasi-Hamiltonian spaces

Abstract: Jeffrey and Kirwan gave expressions for intersection pairings on the reduced space $\mu^{-1}(0)/G$ of a Hamiltonian $G$-space $M$ in terms of iterated residues. The definition of quasi-Hamiltonian spaces was introduced by Alekseev-Malkin-Meinrenken. A localization formula for group valued equivariant de Rham cohomology of a compact $G$-manifold was proved. In this paper we prove a residue formula for intersection pairings of reduced spaces of a quasi-Hamiltonian $G$-space by constructing the corresponding Hamiltonian $G$-spaces. Using Szenes' theorem, we show that the result agrees with the formula given by Alekseev-Meinrenken-Woodward.