Intersection numbers in reduced spaces of quasi-Hamiltonian spaces.
Published: 2004
Language: eng
Number of pages: 99
Description: Jeffrey and Kirwan gave expressions for intersection pairings on the reduced space of a Hamiltonian space in terms of iterated residues. Alekseev, Malkin, and Meinrenken introduced the notion of quasi-Hamiltonian spaces for which the moment map takes values in the group itself rather than in the dual of the Lie algebra, and developed the theory of quasi-Hamiltonian spaces. The theory includes counterparts of Hamiltonian reductions. Alekseev, Meinrenken, and Woodward proved a localization formula for group valued equivariant de Rham cohomology of a compact G-manifold. From this result a Duistermaat-Heckman formula for group valued moment maps was derived.In this paper, we construct the Hamiltonian space corresponding to a given quasi-Hamiltonian space. We use an important property of the Hamiltonian spaces: periodicity. We first prove a residue formula for intersection numbers in the reduced space of a quasi-Hamiltonian T-space (where  T is a compact torus) by induction on r, the rank of T. From that result, we prove a residue formula for intersection pairings of the reduced spaces of a quasi-Hamiltonian G-space (where G is a compact Lie group). We show that the result agrees with that in Alekseev-Meinrenken-Woodward. We rely heavily on the method of Jeffrey and Kirwan (Intersection theory on moduli spaces, which is the reduced space of the quasi-Hamiltonian SU(n)-space  SU(n)2g). For the more general class of compact Lie group, we make use of the result on diagonal bases given by Szenes and Brion-Vergne.
Notes: Adviser:  Lisa Jeffrey.

Thesis (Ph.D.)--University of Toronto, 2004.

Electronic version licensed for access by U. of T. users.

Source: Dissertation Abstracts International, Volume: 65-10, Section: B, page: 5184.