{
  "id": "1605.01192",
  "version": "v1",
  "published": "2016-05-04T09:30:02.000Z",
  "updated": "2016-05-04T09:30:02.000Z",
  "title": "Admitting a coarse embedding is not preserved under group extensions",
  "authors": [
    "Goulnara Arzhantseva",
    "Romain Tessera"
  ],
  "comment": "15 pages",
  "categories": [
    "math.GR",
    "math.FA",
    "math.MG"
  ],
  "abstract": "We construct a finitely generated group which is an extension of two groups coarsely embeddable into Hilbert space but which itself does not coarsely embed into Hilbert space. Our construction also provides a new infinite monster group: the first example of a finitely generated group that does not coarsely embed into Hilbert space and yet does not contain a weakly embedded expander.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-04T09:30:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B85",
      "20F69",
      "22D10",
      "20E22"
    ],
    "keywords": [
      "group extensions",
      "coarse embedding",
      "hilbert space",
      "finitely generated group",
      "infinite monster group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}