{
  "id": "math/0303225",
  "version": "v2",
  "published": "2003-03-18T18:05:15.000Z",
  "updated": "2004-03-02T02:05:34.000Z",
  "title": "Knot Floer homology, genus bounds, and mutation",
  "authors": [
    "Peter Ozsvath",
    "Zolta Szabo"
  ],
  "comment": "minor revisions, updated references",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-03-02T02:05:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R58",
      "53D40"
    ],
    "keywords": [
      "knot floer homology",
      "genus bounds",
      "seifert fibered surgeries",
      "specific families",
      "kinoshita-terasaka knots"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......3225O"
    }
  }
}