{
  "id": "1407.0487",
  "version": "v1",
  "published": "2014-07-02T09:03:39.000Z",
  "updated": "2014-07-02T09:03:39.000Z",
  "title": "Neighbors of Seifert surgeries on a trefoil knot in the Seifert Surgery Network",
  "authors": [
    "Arnaud Deruelle",
    "Katura Miyazaki",
    "Kimihiko Motegi"
  ],
  "comment": "To appear in Bol. Soc. Mat. Mexicana",
  "categories": [
    "math.GT"
  ],
  "abstract": "A Seifert surgery is a pair (K, m) of a knot K in the 3-sphere and an integer m such that m-Dehn surgery on K results in a Seifert fiber space allowed to contain fibers of index zero. Twisting K along a trivial knot called a seiferter for (K, m) yields Seifert surgeries. We study Seifert surgeries obtained from those on a trefoil knot by twisting along their seiferters. Although Seifert surgeries on a trefoil knot are the most basic ones, this family is rich in variety. For any m which is not -2 it contains a successive triple of Seifert surgeries (K, m), (K, m +1), (K, m +2) on a hyperbolic knot K, e.g. 17-, 18-, 19-surgeries on the (-2, 3, 7) pretzel knot. It contains infinitely many Seifert surgeries on strongly invertible hyperbolic knots none of which arises from the primitive/Seifert-fibered construction, e.g. (-1)-surgery on the (3, -3, -3) pretzel knot.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-02T09:03:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M50",
      "57N10"
    ],
    "keywords": [
      "seifert surgery network",
      "trefoil knot",
      "pretzel knot",
      "yields seifert surgeries",
      "study seifert surgeries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.0487D"
    }
  }
}