{
  "id": "1107.2493",
  "version": "v2",
  "published": "2011-07-13T09:10:34.000Z",
  "updated": "2011-08-04T21:32:01.000Z",
  "title": "Fundamental group of uniquely ergodic Cantor minimal systems",
  "authors": [
    "Norio Nawata"
  ],
  "comment": "11 pages",
  "categories": [
    "math.DS",
    "math.OA"
  ],
  "abstract": "We introduce the fundamental group ${\\mathcal F}(\\mathcal{R}_{G, \\phi})$ of a uniquely ergodic Cantor minimal $G$-system $\\mathcal{R}_{G, \\phi}$ where $G$ is a countable discrete group. We compute fundamental groups of several uniquely ergodic Cantor minimal $G$-systems. We show that if $\\mathcal{R}_{G, \\phi}$ arises from a free action $\\phi$ of a finitely generated abelian group, then there exists a unital countable subring $R$ of $\\mathbb{R}$ such that $\\mathcal{F}(\\mathcal{R}_{G, \\phi})=R_{+}^\\times$. We also consider the relation between fundamental groups of uniquely ergodic Cantor minimal $\\mathbb{Z}^n$-systems and fundamental groups of crossed product $C^*$-algebras $C(X)\\rtimes_{\\phi} \\mathbb{Z}^n$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-08-04T21:32:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37A20",
      "46L55"
    ],
    "keywords": [
      "uniquely ergodic cantor minimal systems",
      "fundamental group",
      "countable discrete group",
      "free action",
      "finitely generated abelian group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.2493N"
    }
  }
}