{
  "id": "math/0509039",
  "version": "v2",
  "published": "2005-09-02T14:20:09.000Z",
  "updated": "2009-03-01T21:07:40.000Z",
  "title": "Refined Kirby calculus for integral homology spheres",
  "authors": [
    "Kazuo Habiro"
  ],
  "comment": "This is the version published by Geometry & Topology on 18 September 2006",
  "journal": "Geom. Topol. 10 (2006) 1285-1317",
  "doi": "10.2140/gt.2006.10.1285",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "A theorem of Kirby states that two framed links in the 3-sphere produce orientation-preserving homeomorphic results of surgery if they are related by a sequence of stabilization and handle-slide moves. The purpose of the present paper is twofold: First, we give a sufficient condition for a sequence of handle-slides on framed links to be able to be replaced with a sequences of algebraically canceling pairs of handle-slides. Then, using the first result, we obtain a refinement of Kirby's calculus for integral homology spheres which involves only +/-1-framed links with zero linking numbers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-01T21:07:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "integral homology spheres",
      "refined kirby calculus",
      "produce orientation-preserving homeomorphic results",
      "framed links",
      "kirby states"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9039H"
    }
  }
}