{
  "id": "math/0110176",
  "version": "v2",
  "published": "2001-10-17T15:17:21.000Z",
  "updated": "2003-05-22T17:22:15.000Z",
  "title": "On uniqueness of JSJ decompositions of finitely generated groups",
  "authors": [
    "Max Forester"
  ],
  "comment": "11 pages; shortened and reorganized; mathematical content unchanged",
  "journal": "Comment. Math. Helv. 78 (2003) 740-751",
  "doi": "10.1007/s00014-003-0780-y",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We give an example of two JSJ decompositions of a group that are not related by conjugation, conjugation of edge-inclusions, and slide moves. This answers the question of Rips and Sela stated in \"Cyclic splittings of finitely presented groups and the canonical JSJ decomposition,\" Ann. of Math. 146 (1997), 53-109. On the other hand we observe that any two JSJ decompositions of a group are related by an elementary deformation, and that strongly slide-free JSJ decompositions are genuinely unique. These results hold for the decompositions of Rips and Sela, Dunwoody and Sageev, and Fujiwara and Papasoglu, and also for accessible decompositions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-05-22T17:22:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20E08",
      "57M07"
    ],
    "keywords": [
      "finitely generated groups",
      "uniqueness",
      "strongly slide-free jsj decompositions",
      "cyclic splittings",
      "canonical jsj decomposition"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10176F"
    }
  }
}