{
  "id": "0911.3173",
  "version": "v3",
  "published": "2009-11-16T22:06:10.000Z",
  "updated": "2016-03-25T09:00:11.000Z",
  "title": "JSJ decompositions: definitions, existence, uniqueness. I: The JSJ deformation space",
  "authors": [
    "Vincent Guirardel",
    "Gilbert Levitt"
  ],
  "comment": "This paper and its companion arXiv:1002.4564 have been replaced by arXiv:1602.05139",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "This paper and its companion arXiv:1002.4564 have been replaced by arXiv:1602.05139. We give a general simple definition of JSJ decompositions by means of a universal maximality property. The JSJ decomposition should not be viewed as a tree (which is not uniquely defined) but as a canonical deformation space of trees. We prove that JSJ decompositions of finitely presented groups always exist, without any assumption on edge groups. Many examples are given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-10-15T07:28:54.000Z",
      "abstract": "We give a general simple definition of JSJ decompositions by means of a universal maximality property. The JSJ decomposition should not be viewed as a tree (which is not uniquely defined) but as a canonical deformation space of trees. We prove that JSJ decompositions of finitely presented groups always exist, without any assumption on edge groups. Many examples are given.",
      "comment": "Small changes in the paper organisation. 30 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-03-25T09:00:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E08",
      "20E34",
      "20F65",
      "57M07",
      "20E06"
    ],
    "keywords": [
      "jsj decomposition",
      "jsj deformation space",
      "uniqueness",
      "general simple definition",
      "universal maximality property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.3173G"
    }
  }
}