The K-theory of abelian symplectic quotients

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dc.creatorHarada, Megumi
dc.creatorLandweber, Gregory D.
dc.date2006-12-21
dc.date2008-01-02
dc.date.accessioned2026-07-07T08:51:45Z
dc.date.available2026-07-07T08:51:45Z
dc.descriptionLet T be a compact torus and (M,ω) a Hamiltonian T-space. In a previous paper, the authors showed that the T-equivariant K-theory of the manifold M surjects onto the ordinary integral K-theory of the symplectic quotient M \mod T of M by T, under certain technical conditions on the moment map. In this paper, we use equivariant Morse theory to give a method for computing the K-theory of the symplectic quotient by obtaining an explicit description of the kernel of the surjection κ: K^*_T(M) \onto K^*(M \mod T). Our results are K-theoretic analogues of the work of Tolman and Weitsman for Borel equivariant cohomology. Further, we prove that under suitable technical conditions on the T-orbit stratification of M, there is an explicit Goresky-Kottwitz-MacPherson (``GKM'') type combinatorial description of the K-theory of a Hamiltonian T-space in terms of fixed point data. Finally, we illustrate our methods by computing the ordinary K-theory of compact symplectic toric manifolds, which arise as symplectic quotients of an affine space \C^N by a linear torus action.
dc.description15 pages; typos corrected
dc.identifierhttps://arxiv.org/abs/math/0612660
dc.identifierhttp://arxiv.org/abs/math/0612660
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145044
dc.subjectSymplectic Geometry
dc.subjectK-Theory and Homology
dc.subject53D20; 19L47
dc.titleThe K-theory of abelian symplectic quotients
dc.typetext

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