{
  "id": "1706.07729",
  "version": "v1",
  "published": "2017-06-23T14:41:59.000Z",
  "updated": "2017-06-23T14:41:59.000Z",
  "title": "An overview of knot Floer homology",
  "authors": [
    "Peter Ozsvath",
    "Zoltan Szabo"
  ],
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "Knot Floer homology is an invariant for knots discovered by the authors and, independently, Jacob Rasmussen. The discovery of this invariant grew naturally out of studying how a certain three-manifold invariant, Heegaard Floer homology, changes as the three-manifold undergoes Dehn surgery along a knot. Since its original definition, thanks to the contributions of many researchers, knot Floer homology has emerged as a useful tool for studying knots in its own right. We give here a few selected highlights of this theory, and then move on to some new algebraic developments in the computation of knot Floer homology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-23T14:41:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R58",
      "57M25"
    ],
    "keywords": [
      "knot floer homology",
      "three-manifold undergoes dehn surgery",
      "heegaard floer homology",
      "jacob rasmussen",
      "invariant grew"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}