{
  "id": "1204.4193",
  "version": "v3",
  "published": "2012-04-18T20:05:13.000Z",
  "updated": "2012-12-03T18:34:34.000Z",
  "title": "Quasi-isometric co-Hopficity of non-uniform lattices in rank-one semi-simple Lie groups",
  "authors": [
    "Ilya Kapovich",
    "Anton Lukyanenko"
  ],
  "comment": "13 pages, 2 figures",
  "journal": "Conform. Geom. Dyn. 16 (2012), 269-282",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We prove that if $G$ is a non-uniform lattice in a rank-one semi-simple Lie group $\\ne Isom(\\H^2_\\R)$ then $G$ is quasi-isometrically co-Hopf. This means that every quasi-isometric embedding $G\\to G$ is coarsely onto and thus is a quasi-isometry.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-12-03T18:34:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "rank-one semi-simple lie group",
      "non-uniform lattice",
      "quasi-isometric co-hopficity",
      "quasi-isometrically co-hopf"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Conform. Geom. Dyn."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.4193K"
    }
  }
}