{
  "id": "1705.06725",
  "version": "v1",
  "published": "2017-05-18T17:52:49.000Z",
  "updated": "2017-05-18T17:52:49.000Z",
  "title": "Straightening warped cones",
  "authors": [
    "Damian Sawicki",
    "Jianchao Wu"
  ],
  "comment": "17 pages",
  "categories": [
    "math.MG",
    "math.DS",
    "math.GR"
  ],
  "abstract": "We provide converses to two results of J. Roe (Geom. Topol. 2005): first, the warped cone over a free action of a Haagerup group admits a fibred coarse embedding into a Hilbert space, and second, a free action yielding a warped cone with property A must be amenable. We construct examples showing that in both cases the freeness assumption is necessary. The first equivalence is obtained also for other classes of Banach spaces, e.g. for $L^p$-spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-18T17:52:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "straightening warped cones",
      "free action",
      "haagerup group admits",
      "first equivalence",
      "freeness assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}