{
  "id": "1304.0391",
  "version": "v2",
  "published": "2013-04-01T16:36:37.000Z",
  "updated": "2014-11-21T02:13:51.000Z",
  "title": "Injectivity radii of hyperbolic integer homology 3-spheres",
  "authors": [
    "Jeffrey F. Brock",
    "Nathan M. Dunfield"
  ],
  "comment": "29 pages, 11 figures. v2: Incorporates referee's comments. To appear in Geometry and Topology",
  "categories": [
    "math.GT",
    "math.DG",
    "math.NT"
  ],
  "abstract": "We construct hyperbolic integer homology 3-spheres where the injectivity radius is arbitrarily large for nearly all points of the manifold. As a consequence, there exists a sequence of closed hyperbolic 3-manifolds which Benjamini-Schramm converge to H^3 whose normalized Ray-Singer analytic torsions do not converge to the L^2-analytic torsion of H^3. This contrasts with the work of Abert et. al. who showed that Benjamini-Schramm convergence forces convergence of normalized betti numbers. Our results shed light on a conjecture of Bergeron and Venkatesh on the growth of torsion in the homology of arithmetic hyperbolic 3-manifolds, and we give experimental results which support this and related conjectures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-01T16:36:37.000Z",
      "comment": "28 pages, 11 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-21T02:13:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "30F40"
    ],
    "keywords": [
      "injectivity radius",
      "benjamini-schramm convergence forces convergence",
      "construct hyperbolic integer homology",
      "normalized ray-singer analytic torsions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.0391B"
    }
  }
}