{
  "id": "math/0306398",
  "version": "v1",
  "published": "2003-06-27T15:06:33.000Z",
  "updated": "2003-06-27T15:06:33.000Z",
  "title": "Hyperbolic manifolds with geodesic boundary which are determined by their fundamental group",
  "authors": [
    "Roberto Frigerio"
  ],
  "comment": "12 pages, 1 figure",
  "journal": "(revised version) Topology Appl. 145 (2004), 69--81",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let M and N be n-dimensional connected orientable finite-volume hyperbolic manifolds with geodesic boundary, and let f be a given isomorphism between the fundamental groups of M and N. We study the problem whether there exists an isometry between M and N which induces f. We show that this is always the case if the dimension of M and N is at least four, while in the three-dimensional case the existence of an isometry inducing f is proved under some (necessary) additional conditions on f. Such conditions are trivially satisfied if the boundaries of M and N are both compact.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-06-27T15:06:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30F40",
      "57N16"
    ],
    "keywords": [
      "geodesic boundary",
      "fundamental group",
      "connected orientable finite-volume hyperbolic manifolds",
      "n-dimensional connected orientable finite-volume hyperbolic"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......6398F"
    }
  }
}