{
  "id": "1512.05481",
  "version": "v1",
  "published": "2015-12-17T06:55:07.000Z",
  "updated": "2015-12-17T06:55:07.000Z",
  "title": "The volume of hyperbolic cone-manifolds of the knot with Conway's notation $C(2n, 3)$",
  "authors": [
    "Ji-Young Ham",
    "Joongul Lee"
  ],
  "comment": "10 pages, 3 figures. arXiv admin note: text overlap with arXiv:1403.1941",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $C(2n, 3)$ be the family of two bridge knots of slope $(4n+1)/(6n+1)$. We calculate the volumes of the $C(2n, 3)$ cone-manifolds using the Schl\\\"{a}fli formula. We present the concrete and explicit formula of them. We apply the general instructions of Hilden, Lozano, and Montesinos-Amilibia and extend the Ham, Mednykh, and Petrov's methods. As an application, we give the volumes of the cyclic coverings over those knots. For the fundamental group of $C( 2n, 3)$, we take and tailor Hoste and Shanahan's. As a byproduct, we give an affirmative answer for their question whether their presentation is actually derived from Schubert's canonical 2-bridge diagram or not.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-17T06:55:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "hyperbolic cone-manifolds",
      "conways notation",
      "bridge knots",
      "tailor hoste",
      "explicit formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151205481H"
    }
  }
}