{
  "id": "math/0301284",
  "version": "v3",
  "published": "2003-01-24T15:58:52.000Z",
  "updated": "2003-05-22T20:15:39.000Z",
  "title": "A very short proof of Forester's rigidity result",
  "authors": [
    "Vincent Guirardel"
  ],
  "comment": "Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper10.abs.html",
  "journal": "Geom. Topol. 7(2003) 321-328",
  "categories": [
    "math.GR"
  ],
  "abstract": "The deformation space of a simplicial G-tree T is the set of G-trees which can be obtained from T by some collapse and expansion moves, or equivalently, which have the same elliptic subgroups as T. We give a short proof of a rigidity result by Forester which gives a sufficient condition for a deformation space to contain an Aut(G)-invariant G-tree. This gives a sufficient condition for a JSJ splitting to be invariant under automorphisms of G. More precisely, the theorem claims that a deformation space contains at most one strongly slide-free G-tree, where strongly slide-free means the following: whenever two edges e_1, e_2 incident on a same vertex v are such that G_{e_1} is a subset of G_{e_2}, then e_1 and e_2 are in the same orbit under G_v.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-05-22T20:15:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E08",
      "57M07",
      "20F65"
    ],
    "keywords": [
      "foresters rigidity result",
      "short proof",
      "sufficient condition",
      "deformation space contains",
      "theorem claims"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......1284G"
    }
  }
}