# University of Toronto's Symplectic Geometry Seminar

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

SS5017A

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Joon-Hyeok Song

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U of Toronto

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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.