{
  "id": "math/0611173",
  "version": "v3",
  "published": "2006-11-07T09:46:45.000Z",
  "updated": "2007-09-28T09:23:00.000Z",
  "title": "Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems",
  "authors": [
    "Sergey Bezuglyi",
    "Konstantin Medynets"
  ],
  "comment": "17 pages, references added, some typos fixed",
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "In the paper, we consider the full group $[\\phi]$ and topological full group $[[\\phi]]$ of a Cantor minimal system $(X,\\f)$. We prove that the commutator subgroups $D([\\f])$ and $D([[\\f]])$ are simple and show that the groups $D([\\f])$ and $D([[\\f]])$ completely determine the class of orbit equivalence and flip conjugacy of $\\f$, respectively. These results improve the classification found in \\cite{gps:1999}. As a corollary of the technique used, we establish the fact that $\\f$ can be written as a product of three involutions from $[\\f]$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-09-28T09:23:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "20B99"
    ],
    "keywords": [
      "cantor minimal system",
      "flip conjugacy",
      "orbit equivalence",
      "topological full group",
      "commutator subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11173B"
    }
  }
}