{
  "id": "0909.3528",
  "version": "v2",
  "published": "2009-09-18T20:30:54.000Z",
  "updated": "2011-06-26T09:30:33.000Z",
  "title": "C$^*$-simple groups: amalgamated free products, HNN extensions, and fundamental groups of 3-manifolds",
  "authors": [
    "Pierre de la Harpe",
    "Jean-Philippe Préaux"
  ],
  "comment": "43 pages",
  "journal": "Journal of Topology & Analysis, 3 (4), (2011), pp. 451-489",
  "doi": "10.1142/S1793525311000659",
  "categories": [
    "math.GR",
    "math.OA"
  ],
  "abstract": "We establish sufficient conditions for the C$^*$-simplicity of two classes of groups. The first class is that of groups acting on trees, such as amalgamated free products, HNN-extensions, and their normal subgroups; for example normal subgroups of Baumslag-Solitar groups. The second class is that of fundamental groups of compact 3-manifolds, related to the first class by their Kneser-Milnor and JSJ-decompositions. Much of our analysis deals with conditions on an action of a group $\\Gamma$ on a tree $T$ which imply the following three properties: abundance of hyperbolic elements, better called strong hyperbolicity, minimality, both on the tree $T$ and on its boundary $\\partial T$, and faithfulness in a strong sense. An important step in this analysis is to identify automorphism of $T$ which are \\emph{slender}, namely such that their fixed-point sets in $\\partial T$ are nowhere dense for the shadow topology.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-26T09:30:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22D25",
      "20E08",
      "20F65",
      "57N10"
    ],
    "keywords": [
      "amalgamated free products",
      "fundamental groups",
      "hnn extensions",
      "simple groups",
      "first class"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.3528D"
    }
  }
}