{
  "id": "1103.1601",
  "version": "v1",
  "published": "2011-03-08T18:54:05.000Z",
  "updated": "2011-03-08T18:54:05.000Z",
  "title": "Fibered knots and potential counterexamples to the Property 2R and Slice-Ribbon Conjectures",
  "authors": [
    "Robert E. Gompf",
    "Martin Scharlemann",
    "Abigail Thompson"
  ],
  "comment": "Combines and expands arXiv:0908.2795 and arXiv:0901.2319 into the version published in Geometry and Topology",
  "journal": "Geometry & Topology 14 (2010) 2305-2347",
  "categories": [
    "math.GT"
  ],
  "abstract": "If there are any 2-component counterexamples to the Generalized Property R Conjecture, a least genus component of all such counterexamples cannot be a fibered knot. Furthermore, the monodromy of a fibered component of any such counterexample has unexpected restrictions. The simplest plausible counterexample to the Generalized Property R Conjecture could be a 2-component link containing the square knot. We characterize all two-component links that contain the square knot and which surger to (S^1 x S^2) # (S^1 x S^2). We exhibit a family of such links that are probably counterexamples to Generalized Property R. These links can be used to generate slice knots that are not known to be ribbon.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-08T18:54:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57N13"
    ],
    "keywords": [
      "fibered knot",
      "property 2r",
      "slice-ribbon conjectures",
      "potential counterexamples",
      "generalized property"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.1601G"
    }
  }
}