Knot Floer homology, genus bounds, and mutation
| dc.creator | Ozsvath, Peter | |
| dc.creator | Szabo, Zolta | |
| dc.date | 2003-03-18 | |
| dc.date | 2004-03-02 | |
| dc.date.accessioned | 2026-07-07T04:56:10Z | |
| dc.date.available | 2026-07-07T04:56:10Z | |
| dc.description | In an earlier paper, we introduced a collection of graded Abelian groups $\HFKa(Y,K)$ associated to knots in a three-manifold. The aim of the present paper is to investigate these groups for several specific families of knots, including the Kinoshita-Terasaka knots and their ``Conway mutants''. These results show that $\HFKa$ contains more information than the Alexander polynomial and the signature of these knots; and they also illustrate the fact that $\HFKa$ detects mutation. We also calculate $\HFKa$ for certain pretzel knots, and knots with small crossing number ($n\leq 9$). Our calculations prove that many of the knots considered here admit no Seifert fibered surgeries. | |
| dc.description | minor revisions, updated references | |
| dc.identifier | https://arxiv.org/abs/math/0303225 | |
| dc.identifier | http://arxiv.org/abs/math/0303225 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66827 | |
| dc.subject | Geometric Topology | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 57R58, 57M, 53D40 | |
| dc.title | Knot Floer homology, genus bounds, and mutation | |
| dc.type | text |