Giroux correspondence, confoliations, and symplectic structures on S^1 x M
| dc.creator | Kim, Jin Hong | |
| dc.date | 2008-11-05 | |
| dc.date | 2009-01-06 | |
| dc.date.accessioned | 2026-07-07T12:24:26Z | |
| dc.date.available | 2026-07-07T12:24:26Z | |
| dc.description | Let M be a closed oriented 3-manifold such that S^1 x M admits a symplectic structure w. The goal of this paper is to show that M is a fiber bundle over S^1. The basic idea is to use the obvious S^1-action on S^1 x M by rotating the first factor, and one of the key steps is to show that the S^1-action on S^1 x M is actually symplectic with respect to a symplectic form cohomologous to w. We achieve it by crucially using the recent result or its relative version of Giroux about one-to-one correspondence between open book decompositions of M up to positive stabilization and co-oriented contact structures on M up to contact isotopy. | |
| dc.description | 17 pages; Sec.3 rewritten for more clarity | |
| dc.identifier | https://arxiv.org/abs/0811.0641 | |
| dc.identifier | http://arxiv.org/abs/0811.0641 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/214325 | |
| dc.subject | Geometric Topology | |
| dc.subject | Symplectic Geometry | |
| dc.title | Giroux correspondence, confoliations, and symplectic structures on S^1 x M | |
| dc.type | text |