On cohomology of invariant submanifolds of Hamiltonian actions
| dc.creator | Ozan, Yildiray | |
| dc.date | 2003-09-17 | |
| dc.date | 2005-03-15 | |
| dc.date.accessioned | 2026-07-07T05:01:13Z | |
| dc.date.available | 2026-07-07T05:01:13Z | |
| dc.description | In 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.description | 6 pages, corrected typos | |
| dc.identifier | https://arxiv.org/abs/math/0309288 | |
| dc.identifier | http://arxiv.org/abs/math/0309288 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68597 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53D05, 53D12 (Primary), 57R91 (Secondary) | |
| dc.title | On cohomology of invariant submanifolds of Hamiltonian actions | |
| dc.type | text |