{
  "id": "math/0301149",
  "version": "v4",
  "published": "2003-01-14T21:20:03.000Z",
  "updated": "2003-11-18T20:56:51.000Z",
  "title": "Knot Floer homology and the four-ball genus",
  "authors": [
    "Peter Ozsvath",
    "Zoltan Szabo"
  ],
  "comment": "Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper17.abs.html",
  "journal": "Geom. Topol. 7(2003) 615-639",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We use the knot filtration on the Heegaard Floer complex to define an integer invariant tau(K) for knots. Like the classical signature, this invariant gives a homomorphism from the knot concordance group to Z. As such, it gives lower bounds for the slice genus (and hence also the unknotting number) of a knot; but unlike the signature, tau gives sharp bounds on the four-ball genera of torus knots. As another illustration, we calculate the invariant for several ten-crossing knots.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2003-11-18T20:56:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R58",
      "57M25",
      "57M27"
    ],
    "keywords": [
      "knot floer homology",
      "four-ball genus",
      "heegaard floer complex",
      "knot concordance group",
      "integer invariant tau"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......1149O"
    }
  }
}