{
  "id": "1805.02357",
  "version": "v1",
  "published": "2018-05-07T06:17:36.000Z",
  "updated": "2018-05-07T06:17:36.000Z",
  "title": "Treewidth, crushing, and hyperbolic volume",
  "authors": [
    "Clément Maria",
    "Jessica S. Purcell"
  ],
  "comment": "18 pages, 11 figures",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "We prove that there exists a universal constant $c$ such that any closed hyperbolic 3-manifold admits a triangulation of treewidth at most $c$ times its volume. The converse is not true: we show there exists a sequence of hyperbolic 3-manifolds of bounded treewidth but volume approaching infinity. Along the way, we prove that crushing a normal surface in a triangulation does not increase the carving-width, and hence crushing any number of normal surfaces in a triangulation affects treewidth by at most a constant multiple.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-07T06:17:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57Q15",
      "57M15"
    ],
    "keywords": [
      "hyperbolic volume",
      "normal surface",
      "triangulation affects treewidth",
      "volume approaching infinity",
      "constant multiple"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}