{
  "id": "math/0210308",
  "version": "v2",
  "published": "2002-10-19T19:25:50.000Z",
  "updated": "2004-08-27T18:40:12.000Z",
  "title": "Acylindrical accessibility for groups acting on $\\mathbf R$-trees",
  "authors": [
    "Ilya Kapovich",
    "Richard Weidmann"
  ],
  "comment": "Final revised version, to appear in Math. Z",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We prove an acylindrical accessibility theorem for finitely generated groups acting on $\\mathbf R$-trees. Namely, we show that if $G$ is a freely indecomposable non-cyclic $k$-generated group acting minimally and $M$-acylindrically on an $\\mathbf R$-tree $X$ then for any $\\epsilon>0$ there is a finite subtree $Y_{\\epsilon}\\subseteq X$ of measure at most $2M(k-1)+\\epsilon$ such that $GY_{\\epsilon}=X$. This generalizes theorems of Z.Sela and T.Delzant about actions on simplicial trees.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-08-27T18:40:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F67"
    ],
    "keywords": [
      "groups acting",
      "simplicial trees",
      "acylindrical accessibility theorem",
      "finite subtree",
      "generalizes theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10308K"
    }
  }
}