{
  "id": "math/0406607",
  "version": "v2",
  "published": "2004-06-29T15:56:05.000Z",
  "updated": "2005-01-19T13:49:45.000Z",
  "title": "Finite Groups and Hyperbolic Manifolds",
  "authors": [
    "M. Belolipetsky",
    "A. Lubotzky"
  ],
  "comment": "12 pages, to appear in Invent. Math",
  "doi": "10.1007/s00222-005-0446-z",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "The isometry group of a compact n-dimensional hyperbolic manifold is known to be finite. We show that for every n > 2, every finite group is realized as the full isometry group of some compact hyperbolic n-manifold. The cases n = 2 and n = 3 have been proven by Greenberg and Kojima, respectively. Our proof is non constructive: it uses counting results from subgroup growth theory and the strong approximation theorem to show that such manifolds exist.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-01-19T13:49:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57S25",
      "20E07",
      "20G30"
    ],
    "keywords": [
      "finite group",
      "compact n-dimensional hyperbolic manifold",
      "full isometry group",
      "compact hyperbolic n-manifold",
      "subgroup growth theory"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Inventiones Mathematicae",
      "year": 2005,
      "month": "Jun",
      "volume": 162,
      "number": 3,
      "pages": 459
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005InMat.162..459B"
    }
  }
}