{
  "id": "math/0306306",
  "version": "v5",
  "published": "2003-06-20T09:54:21.000Z",
  "updated": "2004-11-29T22:16:32.000Z",
  "title": "Limit groups and groups acting freely on R^n-trees",
  "authors": [
    "Vincent Guirardel"
  ],
  "comment": "Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper39.abs.html",
  "journal": "Geometry and Toplogy 8 (2004) 1427--1470",
  "doi": "10.2140/gt.2004.8.1427",
  "categories": [
    "math.GR",
    "math.GT",
    "math.LO"
  ],
  "abstract": "We give a simple proof of the finite presentation of Sela's limit groups by using free actions on R^n-trees. We first prove that Sela's limit groups do have a free action on an R^n-tree. We then prove that a finitely generated group having a free action on an R^n-tree can be obtained from free abelian groups and surface groups by a finite sequence of free products and amalgamations over cyclic groups. As a corollary, such a group is finitely presented, has a finite classifying space, its abelian subgroups are finitely generated and contains only finitely many conjugacy classes of non-cyclic maximal abelian subgroups.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2004-11-29T22:16:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E08",
      "20E26"
    ],
    "keywords": [
      "groups acting",
      "selas limit groups",
      "free action",
      "non-cyclic maximal abelian subgroups",
      "free abelian groups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}