{
  "id": "1705.00834",
  "version": "v1",
  "published": "2017-05-02T07:42:07.000Z",
  "updated": "2017-05-02T07:42:07.000Z",
  "title": "Lamplighter groups, median spaces, and a-T-menability",
  "authors": [
    "Anthony Genevois"
  ],
  "comment": "18 pages. Comments are welcome",
  "categories": [
    "math.GR",
    "math.MG"
  ],
  "abstract": "This paper is dedicated to the proof of the following statement: the wreath product of two groups acting metrically properly on median spaces acts metrically properly on some median space we call space of wreaths. As a consequence of this construction, we deduce that being a-T-menable and acting properly on some CAT(0) cube complex are properties stable under wreath products.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-02T07:42:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67",
      "43A15"
    ],
    "keywords": [
      "lamplighter groups",
      "a-t-menability",
      "wreath product",
      "median spaces acts",
      "cube complex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}