{
  "id": "math/0406402",
  "version": "v2",
  "published": "2004-06-21T13:52:20.000Z",
  "updated": "2005-10-09T10:23:55.000Z",
  "title": "On knot Floer homology and cabling",
  "authors": [
    "Matthew Hedden"
  ],
  "comment": "Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-48.abs.html",
  "journal": "Algebr. Geom. Topol. 5 (2005) 1197-1222",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "This paper is devoted to the study of the knot Floer homology groups HFK(S^3,K_{2,n}), where K_{2,n} denotes the (2,n) cable of an arbitrary knot, K. It is shown that for sufficiently large |n|, the Floer homology of the cabled knot depends only on the filtered chain homotopy type of CFK(K). A precise formula for this relationship is presented. In fact, the homology groups in the top 2 filtration dimensions for the cabled knot are isomorphic to the original knot's Floer homology group in the top filtration dimension. The results are extended to (p,pn+-1) cables. As an example we compute HFK((T_{2,2m+1})_{2,2n+1}) for all sufficiently large |n|, where T_{2,2m+1} denotes the (2,2m+1)-torus knot.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-10-09T10:23:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57R58"
    ],
    "keywords": [
      "original knots floer homology group",
      "knot floer homology groups",
      "filtration dimension",
      "sufficiently large",
      "filtered chain homotopy type"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6402H"
    }
  }
}