Kirwan surjectivity in K-theory for Hamiltonian loop group quotients

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dc.creatorHarada, Megumi
dc.creatorSelick, Paul
dc.date2007-12-19
dc.date.accessioned2026-07-07T08:50:22Z
dc.date.available2026-07-07T08:50:22Z
dc.descriptionLet G be a compact Lie group and LG its associated loop group. The main result of this manuscript is a surjectivity theorem from the equivariant K-theory of a Hamiltonian LG-space onto the integral K-theory of its Hamiltonian LG-quotient. Our result is a K-theoretic analogue of previous work in rational Borel-equivariant cohomology of Bott, Tolman, and Weitsman. Our proof techniques differ from that of Bott, Tolman, and Weitsman in that they explicitly use the Borel construction, which we do not have at our disposal in equivariant K-theory; we instead directly construct G-equivariant homotopy equivalences to obtain the necessary isomorphisms in equivariant K-theory. The main theorem should also be viewed as a first step toward a similar theorem in K-theory for quasi-Hamiltonian G-spaces and their associated quasi-Hamiltonian quotients.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/0712.3202
dc.identifierhttp://arxiv.org/abs/0712.3202
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144581
dc.subjectSymplectic Geometry
dc.subjectAlgebraic Topology
dc.subject53D20; 55N15
dc.titleKirwan surjectivity in K-theory for Hamiltonian loop group quotients
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