{
  "id": "math/9811181",
  "version": "v1",
  "published": "1998-11-17T00:00:00.000Z",
  "updated": "1998-11-17T00:00:00.000Z",
  "title": "The boundary of the deformation space of the fundamental group of some hyperbolic 3-manifolds fibering over the circle",
  "authors": [
    "Leonid Potyagailo"
  ],
  "comment": "14 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon1/paper23.abs.html",
  "journal": "Geom. Topol. Monogr. 1 (1998), 479-492",
  "categories": [
    "math.GT"
  ],
  "abstract": "By using Thurston's bending construction we obtain a sequence of faithful discrete representations \\rho _n of the fundamental group of a closed hyperbolic 3-manifold fibering over the circle into the isometry group Iso H^4 of the hyperbolic space H^4. The algebraic limit of \\rho _n contains a finitely generated subgroup F whose 3-dimensional quotient \\Omega (F)/F has infinitely generated fundamental group, where \\Omega (F) is the discontinuity domain of F acting on the sphere at infinity. Moreover F is isomorphic to the fundamental group of a closed surface and contains infinitely many conjugacy classes of maximal parabolic subgroups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-11-17T00:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M10",
      "30F40",
      "20H10",
      "57S30",
      "57M05",
      "30F10",
      "30F35"
    ],
    "keywords": [
      "deformation space",
      "hyperbolic",
      "maximal parabolic subgroups",
      "isometry group iso",
      "conjugacy classes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}