{
  "id": "math/0112102",
  "version": "v2",
  "published": "2001-12-11T12:56:51.000Z",
  "updated": "2002-01-03T02:38:32.000Z",
  "title": "Parameterizations of 1-bridge torus knots",
  "authors": [
    "Doo Ho Choi",
    "Ki Hyoung Ko"
  ],
  "comment": "26 pages, 28 figures, a minor revision",
  "categories": [
    "math.GT"
  ],
  "abstract": "A 1-bridge torus knot in a 3-manifold of genus $\\le 1$ is a knot drawn on a Heegaard torus with one bridge. We give two types of normal forms to parameterize the family of 1-bridge torus knots that are similar to the Schubert's normal form and the Conway's normal form for 2-bridge knots. For a given Schubert's normal form we give algorithms to determine the number of components and to compute the fundamental group of the complement when the normal form determines a knot. We also give a description of the double branched cover of an ambient 3-manifold branched along a 1-bridge torus knot by using its Conway's normal form and obtain an explicit formula for the first homology of the double cover.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-01-03T02:38:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M12"
    ],
    "keywords": [
      "torus knot",
      "schuberts normal form",
      "conways normal form",
      "parameterizations",
      "normal form determines"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....12102C"
    }
  }
}