{
  "id": "1010.4133",
  "version": "v1",
  "published": "2010-10-20T08:49:10.000Z",
  "updated": "2010-10-20T08:49:10.000Z",
  "title": "$C^1$-actions of Baumslag-Solitar groups on $S^1$",
  "authors": [
    "Nancy Guelman",
    "Isabelle Liousse"
  ],
  "journal": "Algebraic & Geometric Topology 11 (2011) 1701-1707",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $BS(1, n)=< a, b | aba^{-1} = b^n >$ be the solvable Baumslag-Solitar group, where $ n\\geq 2$. It is known that B(1, n) is isomorphic to the group generated by the two affine maps of the line : $f_0(x) = x + 1$ and $h_0(x) = nx $. The action on $S^1 = \\RR \\cup {\\infty}$ generated by these two affine maps $f_0$ and $h_0 $ is called the standard affine one. We prove that any representation of BS(1,n) into $Diff^1(S^1)$ is (up to a finite index subgroup) semiconjugated to the standard affine action.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-20T08:49:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37Bxx",
      "37Exx"
    ],
    "keywords": [
      "affine maps",
      "standard affine action",
      "finite index subgroup",
      "solvable baumslag-solitar group",
      "representation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.4133G"
    }
  }
}