{
  "id": "math/0311496",
  "version": "v3",
  "published": "2003-11-27T03:10:30.000Z",
  "updated": "2004-03-03T17:55:28.000Z",
  "title": "Holomorphic disks and genus bounds",
  "authors": [
    "Peter Ozsvath",
    "Zoltan Szabo"
  ],
  "comment": "Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper8.abs.html",
  "journal": "Geom. Topol. 8(2004) 311-334",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We prove that, like the Seiberg-Witten monopole homology, the Heegaard Floer homology for a three-manifold determines its Thurston norm. As a consequence, we show that knot Floer homology detects the genus of a knot. This leads to new proofs of certain results previously obtained using Seiberg-Witten monopole Floer homology (in collaboration with Kronheimer and Mrowka). It also leads to a purely Morse-theoretic interpretation of the genus of a knot. The method of proof shows that the canonical element of Heegaard Floer homology associated to a weakly symplectically fillable contact structure is non-trivial. In particular, for certain three-manifolds, Heegaard Floer homology gives obstructions to the existence of taut foliations.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-03-03T17:55:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R58",
      "53D40",
      "57M27",
      "57N10"
    ],
    "keywords": [
      "heegaard floer homology",
      "genus bounds",
      "holomorphic disks",
      "symplectically fillable contact structure",
      "seiberg-witten monopole floer homology"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11496O"
    }
  }
}