On cohomology of invariant submanifolds of Hamiltonian actions

dc.creatorOzan, Yildiray
dc.date2003-09-17
dc.date2005-03-15
dc.date.accessioned2026-07-07T05:01:13Z
dc.date.available2026-07-07T05:01:13Z
dc.descriptionIn this note we prove the following theorem: Let $G$ be a compact Lie group acting on a compact symplectic manifold $M$ in a Hamiltonian fashion. If $L$ is an $l$-dimensional closed invariant submanifold of $M$, on which the $G$-action is locally free then the fundamental class $[L]$ is trivial in $H_l(M,{\mathbb Q})$. We also prove similar results for lower homology groups of $L$, in case the group $G$ is a finite product of copies of $S^1$ and SU(2). The key ingredients of the proofs are Kirwan's theorem that Hamiltonian spaces are equivariantly formal and symplectic reduction.
dc.description6 pages, corrected typos
dc.identifierhttps://arxiv.org/abs/math/0309288
dc.identifierhttp://arxiv.org/abs/math/0309288
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68597
dc.subjectSymplectic Geometry
dc.subject53D05, 53D12 (Primary), 57R91 (Secondary)
dc.titleOn cohomology of invariant submanifolds of Hamiltonian actions
dc.typetext

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