{
  "id": "1404.1510",
  "version": "v2",
  "published": "2014-04-05T19:37:12.000Z",
  "updated": "2015-09-11T13:33:22.000Z",
  "title": "Classification of joinings for Kleinian groups",
  "authors": [
    "Amir Mohammadi",
    "Hee Oh"
  ],
  "comment": "57 pages, To appear in Duke Math. J",
  "categories": [
    "math.DS"
  ],
  "abstract": "We classify all locally finite joinings of a horospherical subgroup action on \\Gamma \\ G when \\Gamma is a Zariski dense geometrically finite subgroup of G=PSL_2(R) or PSL_2(C). This generalizes Ratner's 1983 joining theorem for the case when \\Gamma is a lattice in G. One of the main ingredients is equidistribution of non-closed horospherical orbits with respect to the Burger-Roblin measure which we prove in a greater generality where G is the connected component of the identity in SO(n,1) for n at least 2 and \\Gamma is any Zariski dense geometrically finite subgroup of G.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-05T19:37:12.000Z",
      "abstract": "We classify all locally finite joinings of a horospherical subgroup action on \\Gamma \\ G when G=PSL_2(R) or PSL_2(C) and Gamma is a geometrically finite Zariski dense subgroup of G. This generalizes Ratner's 1983 joining theorem for the case when \\Gamma is a lattice in G.",
      "comment": "53 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-09-11T13:33:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kleinian groups",
      "geometrically finite zariski dense subgroup",
      "classification",
      "generalizes ratners",
      "locally finite joinings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.1510M"
    }
  }
}