{
  "id": "1302.7011",
  "version": "v1",
  "published": "2013-02-27T21:38:24.000Z",
  "updated": "2013-02-27T21:38:24.000Z",
  "title": "Some knots in S^1 x S^2 with lens space surgeries",
  "authors": [
    "Kenneth L. Baker",
    "Dorothy Buck",
    "Ana G. Lecuona"
  ],
  "comment": "35 pages, 32 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We propose a classification of knots in S^1 x S^2 that admit a longitudinal surgery to a lens space. Any lens space obtainable by longitudinal surgery on some knots in S^1 x S^2 may be obtained from a Berge-Gabai knot in a Heegaard solid torus of S^1 x S^2, as observed by Rasmussen. We show that there are yet two other families of knots: those that lie on the fiber of a genus one fibered knot and the `sporadic' knots. All these knots in S^1 x S^2 are both doubly primitive and spherical braids. This classification arose from generalizing Berge's list of doubly primitive knots in S^3, though we also examine how one might develop it using Lisca's embeddings of the intersection lattices of rational homology balls bounded by lens spaces as a guide. We conjecture that our knots constitute a complete list of doubly primitive knots in S^1 x S^2 and reduce this conjecture to classifying the homology classes of knots in lens spaces admitting a longitudinal S^1 x S^2 surgery.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-27T21:38:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "lens space surgeries",
      "longitudinal surgery",
      "doubly primitive knots",
      "heegaard solid torus",
      "knots constitute"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.7011B"
    }
  }
}