{
  "id": "0902.0014",
  "version": "v1",
  "published": "2009-01-30T21:23:08.000Z",
  "updated": "2009-01-30T21:23:08.000Z",
  "title": "Betti numbers and injectivity radii",
  "authors": [
    "Marc Culler",
    "Peter B. Shalen"
  ],
  "comment": "4 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give lower bounds on the maximal injectivity radius for a closed orientable hyperbolic 3-manifold M with first Betti number 2, under some additional topological hypotheses. A corollary of the main result is that if M has first Betti number 2 and contains no fibroid surface then its maximal injectivity radius exceeds 0.32798. For comparison, Andrew Przeworski showed, with no topological restrictions, that the maximal injectivity radius exceeds arcsinh(1/4) = 0.247..., while the authors showed that if M has first Betti number at least 3 then the maximal injectivity exceeds log(3)/2 = 0.549.... The proof combines a result due to Przeworski with techniques developed by the authors in the 1990s.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-30T21:23:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57N10"
    ],
    "keywords": [
      "first betti number",
      "maximal injectivity radius exceeds arcsinh",
      "maximal injectivity exceeds log",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}