{
  "id": "1703.01324",
  "version": "v1",
  "published": "2017-03-03T20:03:52.000Z",
  "updated": "2017-03-03T20:03:52.000Z",
  "title": "Waist size for cusps in hyperbolic 3-manifolds II",
  "authors": [
    "Colin Adams"
  ],
  "comment": "15 pages, 10 figures",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "The waist size of a cusp in an orientable hyperbolic 3-manifold is the length of the shortest nontrivial curve generated by a parabolic isometry in the maximal cusp boundary. Previously, it was shown that the smallest possible waist size, which is 1, is realized only by the cusp in the figure-eight knot complement. In this paper, it is proved that the next two smallest waist sizes are realized uniquely for the cusps in the $5_2$ knot complement and the manifold obtained by (2,1)-surgery on the Whitehead link. One application is an improvement on the universal upper bound for the length of an unknotting tunnel in a 2-cusped hyperbolic 3-manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-03T20:03:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50"
    ],
    "keywords": [
      "hyperbolic",
      "maximal cusp boundary",
      "shortest nontrivial curve",
      "figure-eight knot complement",
      "smallest waist sizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}