{
  "id": "1005.4084",
  "version": "v3",
  "published": "2010-05-21T21:23:53.000Z",
  "updated": "2011-01-23T07:51:52.000Z",
  "title": "Poincaré inequalities, embeddings, and wild groups",
  "authors": [
    "Assaf Naor",
    "Lior Silberman"
  ],
  "comment": "Minor changes to address comments of a referee. To appear in Compositio Mathematica",
  "doi": "10.1112/S0010437X11005343",
  "categories": [
    "math.GR",
    "math.FA",
    "math.MG"
  ],
  "abstract": "We present geometric conditions on a metric space $(Y,d_Y)$ ensuring that almost surely, any isometric action on $Y$ by Gromov's expander-based random group has a common fixed point. These geometric conditions involve uniform convexity and the validity of nonlinear Poincar\\'e inequalities, and they are stable under natural operations such as scaling, Gromov-Hausdorff limits, and Cartesian products. We use methods from metric embedding theory to establish the validity of these conditions for a variety of classes of metric spaces, thus establishing new fixed point results for actions of Gromov's \"wild groups\".",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-01-23T07:51:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wild groups",
      "metric space",
      "geometric conditions",
      "gromovs expander-based random group",
      "fixed point"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.4084N"
    }
  }
}