An Ozsvath-Szabo Floer homology invariant of knots in a contact manifold
| dc.creator | Hedden, Matthew | |
| dc.date | 2007-08-03 | |
| dc.date | 2007-08-05 | |
| dc.date.accessioned | 2026-07-07T08:22:03Z | |
| dc.date.available | 2026-07-07T08:22:03Z | |
| dc.description | Using the knot Floer homology filtration, we define invariants associated to a knot in a three-manifold possessing non-vanishing Floer co(homology) classes. In the case of the Ozsvath-Szabo contact invariant we obtain an invariant of knots in a contact three-manifold. This invariant provides an upper bound for the Thurston-Bennequin plus rotation number of any Legendrian realization of the knot. We use it to demonstrate the first systematic construction of prime knots in contact manifolds other than the three-sphere with negative maximal Thurston-Bennequin invariant. Perhaps more interesting, our invariant provides a criterion for an open book to induce a tight contact structure. A corollary is that if a manifold possesses contact structures with distinct non-vanishing Ozsvath-Szabo invariants, then any fibered knot can realize the classical Eliashberg-Bennequin bound in at most one of these contact structures. | |
| dc.description | 30 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0708.0448 | |
| dc.identifier | http://arxiv.org/abs/0708.0448 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135522 | |
| dc.subject | Geometric Topology | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 57M27, 57R58 | |
| dc.title | An Ozsvath-Szabo Floer homology invariant of knots in a contact manifold | |
| dc.type | text |