{
  "id": "0710.0357",
  "version": "v2",
  "published": "2007-10-01T18:53:10.000Z",
  "updated": "2007-10-02T18:50:12.000Z",
  "title": "On Floer homology and the Berge conjecture on knots admitting lens space surgeries",
  "authors": [
    "Matthew Hedden"
  ],
  "comment": "25 pages, 4 figures - reference updated, erroneously included figures removed",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-10-02T18:50:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "knots admitting lens space surgeries",
      "berge conjecture",
      "knot floer homology",
      "simple floer homology belong",
      "first step"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.0357H"
    }
  }
}