{
  "id": "1106.6302",
  "version": "v2",
  "published": "2011-06-30T16:53:34.000Z",
  "updated": "2013-01-23T20:55:03.000Z",
  "title": "Rank and genus of 3-manifolds",
  "authors": [
    "Tao Li"
  ],
  "comment": "60 pages, 15 figures. Minor changes, typos corrected",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We construct a counterexample to the Rank versus Genus Conjecture, i.e. a closed orientable hyperbolic 3-manifold with rank of its fundamental group smaller than its Heegaard genus. Moreover, we show that the discrepancy between rank and Heegaard genus can be arbitrarily large for hyperbolic 3-manifolds. We also construct toroidal such examples containing hyperbolic JSJ pieces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-23T20:55:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57M27",
      "57M05"
    ],
    "keywords": [
      "heegaard genus",
      "examples containing hyperbolic jsj pieces",
      "fundamental group smaller",
      "genus conjecture",
      "construct toroidal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.6302L"
    }
  }
}