Intersection numbers in reduced spaces of quasi-Hamiltonian spaces.
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Intersection numbers in reduced spaces of quasi-Hamiltonian spaces. by Joon-Hyeok Song

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Published .
Written in English


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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.

The Physical Object
Pagination99 leaves.
Number of Pages99
ID Numbers
Open LibraryOL19887197M
ISBN 100612944107

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In this paper we prove a residue formula for intersection pairings of reduced spaces of certain quasi-Hamiltonian G-spaces, by constructing the corresponding Hamiltonian :// Witten's Nonabelian Localization for Noncompact Hamiltonian Spaces Article in Differential Geometry and its Applications 25(2) April with 20 Reads How we measure 'reads''s_Nonabelian_Localization.   第七届华人数学家大会会议安排手册_理学_高等教育_教育专区 79人阅读|次下载 第七届华人数学家大会会议安排手册_理学_高等教育_教育专区。 Contents Congress Chairman?://   Also, the genus expansion of the logarithm of the Witten - Kontsevich tau-function of KdV coincides with the generating function of the intersection numbers of certain cycles on the Deligne - Mumford moduli spaces of stable algebraic   Web view.

Thesis title: Volume Formula and Intersection Pairings of N-fold Reduced Products Let $ G $ be a semisimple compact connected Lie group. An $ N $-fold reduced product of $ G $ is the symplectic quotient of the Hamiltonian system of the Cartesian product of $ N $ coadjoint orbits of $ G $ under diagonal coadjoint action of $ G $ Quasi-Hamiltonian spaces, introduced by Alekseev, Malkin, and Meinrenken, are similar to Hamiltonian G-manifolds but with two significant differences: first, the 2-form on the manifold is neither closed nor nondegenerate, but one has control over the image of the differential of the 2-form, as well as the degeneracy locus of the 2-form, and The collection of mean values in the Mean value theorem. reference-request real-analysis measure-theory mean-value-theorem. modified 12 mins ago OOESCoupling 1, Regularity of conformal maps. ential-geometry is-of-pdes x-variables riemannian-geometry conformal-geometry. modified 29 mins ago seub 1,   Here, is the equivariant Cartan 3-form determined by an invariant inner product on the Lie algebra ⁠.The condition that ω be nondegenerate is replaced by the weaker condition that everywhere. Products, conjugates, and reductions are defined similar to the Hamiltonian case. Basic examples of q-Hamiltonian spaces are conjugacy classes ⁠, with moment map being the ://

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