{
  "id": "math/0701618",
  "version": "v2",
  "published": "2007-01-22T16:39:41.000Z",
  "updated": "2008-12-01T21:12:56.000Z",
  "title": "Boundaries and JSJ decompositions of CAT(0)-groups",
  "authors": [
    "Panos Papasoglu",
    "Eric Swenson"
  ],
  "comment": "minor corrections,38 pages, 2 figures, to appear in GAFA",
  "categories": [
    "math.GR",
    "math.GT",
    "math.MG"
  ],
  "abstract": "Let G be a one-ended group acting discretely and co-compactly on a CAT(0) space X. We show that the boundary of X has no cut points and that one can detect splittings of $G$ over two-ended groups and recover its JSJ decomposition from the boundary. We show that any discrete action of a group G on a CAT(0) space X satisfies a convergence type property. This is used in the proof of the results above but it is also of independent interest. In particular, if G acts co-compactly on X, then one obtains as a Corollary that if the Tits diameter of the boundary of X is bigger than $\\frac {3\\pi} 2$ then it is infinite and G contains a free subgroup of rank 2.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-12-01T21:12:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F67",
      "20E06",
      "20E34",
      "57M07"
    ],
    "keywords": [
      "jsj decomposition",
      "convergence type property",
      "cut points",
      "detect splittings",
      "discrete action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1618P"
    }
  }
}