{
  "id": "math/0612830",
  "version": "v2",
  "published": "2006-12-28T15:44:24.000Z",
  "updated": "2007-02-28T14:11:46.000Z",
  "title": "Two-sided bounds for the complexity of cyclic branched coverings of two-bridge links",
  "authors": [
    "Carlo Petronio",
    "Andrei Vesnin"
  ],
  "comment": "Estimates improved using recent results of Gueritaud-Futer and Kim-Kim",
  "journal": "Osaka J. Math. 46 (2009), 1077-1095",
  "categories": [
    "math.GT"
  ],
  "abstract": "We consider closed orientable 3-dimensional hyperbolic manifolds which are cyclic branched coverings of the 3-sphere, with branching set being a two-bridge knot (or link). We establish two-sided linear bounds depending on the order of the covering for the Matveev complexity of the covering manifold. The lower estimate uses the hyperbolic volume and results of Cao-Meyerhoff and Gueritaud-Futer (who recently improved previous work of Lackenby), while the upper estimate is based on an explicit triangulation, which also allows us to give a bound on the Delzant T-invariant of the fundamental group of the manifold.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-02-28T14:11:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M50"
    ],
    "keywords": [
      "cyclic branched coverings",
      "two-bridge links",
      "two-sided bounds",
      "two-sided linear bounds depending",
      "two-bridge knot"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12830P"
    }
  }
}