{
  "id": "1008.2047",
  "version": "v1",
  "published": "2010-08-12T05:22:18.000Z",
  "updated": "2010-08-12T05:22:18.000Z",
  "title": "A lower bound on the width of satellite knots",
  "authors": [
    "Alexander Zupan"
  ],
  "comment": "10 pages, 3 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Thin position for knots in the 3-sphere was introduced by Gabai and has been used in a variety of contexts. We conjecture an analogue to a theorem of Schubert and Schultens concerning the bridge number of satellite knots. For a satellite knot K, we use the companion torus T to provide a lower bound for w(K), proving the conjecture for K with a 2-bridge companion. As a corollary, we find thin position for any satellite knot with a braid pattern and 2-bridge companion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-12T05:22:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "satellite knot",
      "lower bound",
      "thin position",
      "bridge number",
      "companion torus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.2047Z"
    }
  }
}