{
  "id": "1109.2765",
  "version": "v2",
  "published": "2011-09-13T12:54:39.000Z",
  "updated": "2012-05-15T16:00:12.000Z",
  "title": "Separability of double cosets and conjugacy classes in 3-manifold groups",
  "authors": [
    "Emily Hamilton",
    "Henry Wilton",
    "Pavel Zalesskii"
  ],
  "comment": "25 pages; incorporates Agol's solution to the Virtually Haken Conjecture to prove conjugacy separability for all 3-manifold groups; to appear in the Journal of the LMS",
  "doi": "10.1112/jlms/jds040",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Let M = H^3 / \\Gamma be a hyperbolic 3-manifold of finite volume. We show that if H and K are abelian subgroups of \\Gamma and g is in \\Gamma, then the double coset HgK is separable in \\Gamma. As a consequence we prove that if M is a closed, orientable, Haken 3-manifold and the fundamental group of every hyperbolic piece of the torus decomposition of M is conjugacy separable then so is the fundamental group of M. Invoking recent work of Agol and Wise, it follows that if M is a compact, orientable 3-manifold then \\pi_1(M) is conjugacy separable.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-15T16:00:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E26"
    ],
    "keywords": [
      "conjugacy classes",
      "fundamental group",
      "separability",
      "double coset hgk",
      "abelian subgroups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.2765H"
    }
  }
}