{
  "id": "1410.0303",
  "version": "v1",
  "published": "2014-10-01T17:41:53.000Z",
  "updated": "2014-10-01T17:41:53.000Z",
  "title": "Contact structures and reducible surgeries",
  "authors": [
    "Tye Lidman",
    "Steven Sivek"
  ],
  "comment": "33 pages",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We apply results from both contact topology and exceptional surgery theory to study when Legendrian surgery on a knot yields a reducible manifold. As an application, we show that a reducible surgery on a non-cabled positive knot of genus g must have slope 2g-1, leading to a proof of the cabling conjecture for positive knots of genus 2. Our techniques also produce bounds on the maximum Thurston-Bennequin numbers of cables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-01T17:41:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57R17"
    ],
    "keywords": [
      "reducible surgery",
      "contact structures",
      "maximum thurston-bennequin numbers",
      "exceptional surgery theory",
      "knot yields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.0303L"
    }
  }
}