{
  "id": "1312.0278",
  "version": "v2",
  "published": "2013-12-01T21:49:43.000Z",
  "updated": "2014-12-17T18:11:21.000Z",
  "title": "Commability of groups quasi-isometric to trees",
  "authors": [
    "Mathieu Carette"
  ],
  "comment": "22 pages. Final version, incorporating referee's comments. To appear in Annales de L'Institut Fourier",
  "categories": [
    "math.GR",
    "math.MG"
  ],
  "abstract": "Commability is the finest equivalence relation between locally compact groups such that $G$ and $H$ are equivalent whenever there is a continuous proper homomorphism $G \\to H$ with cocompact image. Answering a question of Cornulier, we show that all non-elementary locally compact groups acting geometrically on locally finite simplicial trees are commable, thereby strengthening previous forms of quasi-isometric rigidity for trees. We further show that 6 homomorphisms always suffice, and provide the first example of a pair of locally compact groups which are commable but without commation consisting of less than 6 homomorphisms. Our strong quasi-isometric rigidity also applies to products of symmetric spaces and Euclidean buildings, possibly with some factors being trees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-01T21:49:43.000Z",
      "comment": "22 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-17T18:11:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22D05",
      "20F65",
      "20E08",
      "20E42"
    ],
    "keywords": [
      "groups quasi-isometric",
      "commability",
      "locally compact groups acting",
      "non-elementary locally compact groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.0278C"
    }
  }
}