{
  "id": "1310.2465",
  "version": "v3",
  "published": "2013-10-09T13:19:57.000Z",
  "updated": "2014-05-26T18:40:19.000Z",
  "title": "Actions of solvable Baumslag-Solitar groups on surfaces with (pseudo-)Anosov elements",
  "authors": [
    "Juan Alonso",
    "Nancy Guelman",
    "Juliana Xavier"
  ],
  "comment": "new version with improvements",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $BS(1,n)= <a,b : a b a ^{-1} = b ^n>$ be the solvable Baumslag-Solitar group, where $n \\geq 2$. We study representations of $BS(1, n)$ by homeomorphisms of closed surfaces with (pseudo-)Anosov elements. That is, we consider a closed surface $S$, and homeomorphisms $f, h: S \\to S$ such that $h f h^{-1} = f^n$, for some $ n\\geq 2$. It is known that $f$ (or some power of $f$) must be homotopic to the identity. Suppose that $h$ is pseudo-Anosov with stretch factor $\\lambda >1$. We show that $<f,h>$ is not a faithful representation of $BS(1, n)$ if $\\lambda > n$. Moreover, we show that there are no faithful representations of $BS(1, n)$ by torus homeomorphisms with $h$ an Anosov map and $f$ area preserving (regardless of the value of $\\lambda$).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-26T18:40:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "solvable baumslag-solitar group",
      "anosov elements",
      "closed surface",
      "faithful representation",
      "anosov map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.2465A"
    }
  }
}