{
  "id": "1312.5586",
  "version": "v1",
  "published": "2013-12-19T15:28:23.000Z",
  "updated": "2013-12-19T15:28:23.000Z",
  "title": "Braids and combinatorial knot Floer homology",
  "authors": [
    "Peter Lambert-Cole",
    "Michaela Stone",
    "David Shea Vela-Vick"
  ],
  "comment": "18 pages, 8 figures",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We present a braid-theoretic approach to combinatorially computing knot Floer homology. To a knot or link K, which is braided about the standard disk open book decomposition for (S^3,\\xi_std), we associate a corresponding multi-pointed nice Heegaard diagram. We then describe an explicit algorithm for computing the associated knot Floer homology groups. We compute explicit bounds for the computational complexity of our algorithm and demonstrate that, in many cases, it is significantly faster than the previous approach using grid diagrams.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-19T15:28:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57R58"
    ],
    "keywords": [
      "combinatorial knot floer homology",
      "knot floer homology groups",
      "computing knot floer homology",
      "multi-pointed nice heegaard diagram",
      "standard disk open book decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.5586L"
    }
  }
}