{
  "id": "0904.2698",
  "version": "v1",
  "published": "2009-04-17T13:36:05.000Z",
  "updated": "2009-04-17T13:36:05.000Z",
  "title": "Commensurability and separability of quasiconvex subgroups",
  "authors": [
    "Frederic Haglund"
  ],
  "comment": "This is the version published by Algebraic & Geometric Topology on 9 August 2006",
  "journal": "Algebr. Geom. Topol. 6 (2006) 949-1024",
  "doi": "10.2140/agt.2006.6.949",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We show that two uniform lattices of a regular right-angled Fuchsian building are commensurable, provided the chamber is a polygon with at least six edges. We show that in an arbitrary Gromov-hyperbolic regular right-angled building associated to a graph product of finite groups, a uniform lattice is commensurable with the graph product provided all of its quasiconvex subgroups are separable. We obtain a similar result for uniform lattices of the Davis complex of Gromov-hyperbolic two-dimensional Coxeter groups. We also prove that every extension of a uniform lattice of a CAT(0) square complex by a finite group is virtually trivial, provided each quasiconvex subgroup of the lattice is separable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-17T13:36:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "20F65",
      "20F67",
      "20E22",
      "20E26",
      "20J06",
      "51E24"
    ],
    "keywords": [
      "quasiconvex subgroup",
      "uniform lattice",
      "gromov-hyperbolic regular right-angled building",
      "gromov-hyperbolic two-dimensional coxeter groups",
      "commensurability"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.2698H"
    }
  }
}