On Floer homology and the Berge conjecture on knots admitting lens space surgeries
| dc.creator | Hedden, Matthew | |
| dc.date | 2007-10-01 | |
| dc.date | 2007-10-02 | |
| dc.date.accessioned | 2026-07-07T08:33:20Z | |
| dc.date.available | 2026-07-07T08:33:20Z | |
| dc.description | We complete the first step in a two-part program proposed by Baker, Grigsby, and the author to prove that Berge's construction of knots in the three-sphere which admit lens space surgeries is complete. The first step, which we prove here, is to show that a knot in a lens space with a three-sphere surgery has simple (in the sense of rank) knot Floer homology. The second (conjectured) step involves showing that, for a fixed lens space, the only knots with simple Floer homology belong to a simple finite family. Using results of Baker, we provide evidence for the conjectural part of the program by showing that it holds for a certain family of knots. Coupled with work of Ni, these knots provide the first infinite family of non-trivial knots which are characterized by their knot Floer homology. As another application, we provide a Floer homology proof of a theorem of Berge. | |
| dc.description | 25 pages, 4 figures - reference updated, erroneously included figures removed | |
| dc.identifier | https://arxiv.org/abs/0710.0357 | |
| dc.identifier | http://arxiv.org/abs/0710.0357 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139094 | |
| dc.subject | Geometric Topology | |
| dc.subject | Symplectic Geometry | |
| dc.title | On Floer homology and the Berge conjecture on knots admitting lens space surgeries | |
| dc.type | text |