The Kirwan map, equivariant Kirwan maps, and their kernels

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dc.creatorJeffrey, Lisa C.
dc.creatorMare, Augustin-Liviu
dc.creatorWoolf, Jonathan M.
dc.date2002-11-19
dc.date2005-02-04
dc.date.accessioned2026-07-07T06:32:54Z
dc.date.available2026-07-07T06:32:54Z
dc.descriptionConsider a Hamiltonian action of a compact Lie group K on a compact symplectic manifold. We find descriptions of the kernel of the Kirwan map corresponding to a regular value of the moment map $κ_K$. We start with the case when K is a torus T: we determine the kernel of the equivariant Kirwan map (defined by Goldin in [Go]) corresponding to a generic circle S in T, and show how to recover from this the kernel of $κ_T$, as described by Tolman and Weitsman. (In the situation when the fixed point set of the torus action is finite, similar results have been obtained in our previous papers [Je], [Je-Ma]). For a compact nonabelian Lie group K we will use the ``non-abelian localization formula'' of [Je-Ki1] and [Je-Ki2] to establish relationships -- some of them obtained by Tolman and Weitsman in [To-We] -- between $\ker(κ_K)$ and $\ker(κ_T)$, where T is a maximal torus in K. An Appendix generalizes Theorem 1.8 to the case of singular values of $κ_T$.
dc.description21 pages; appendix on generalization to reduction at singular values added To appear in J. Reine Angew. Math
dc.identifierhttps://arxiv.org/abs/math/0211297
dc.identifierhttp://arxiv.org/abs/math/0211297
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99015
dc.subjectSymplectic Geometry
dc.subjectDifferential Geometry
dc.subject53D99
dc.titleThe Kirwan map, equivariant Kirwan maps, and their kernels
dc.typetext

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