{
  "id": "1509.06688",
  "version": "v1",
  "published": "2015-09-22T17:15:18.000Z",
  "updated": "2015-09-22T17:15:18.000Z",
  "title": "Equivalence of $\\mathbb{Z}_{4}$-actions on handlebodies of genus $g$",
  "authors": [
    "Jesse Prince-Lubawy"
  ],
  "categories": [
    "math.GN",
    "math.AT",
    "math.GT"
  ],
  "abstract": "In this paper we consider all orientation-preserving $\\mathbb{Z}_{4}$-actions on $3$-dimensional handlebodies $V_g$ of genus $g>0$. We study the graph of groups $(\\Gamma($v$),\\mathbf{G(v)})$, which determines a handlebody orbifold $V(\\Gamma($v$),{\\mathbf{G(v)}})\\simeq{V_g}/\\mathbb{Z}_{4}$. This algebraic characterization is used to enumerate the total number of $\\mathbb{Z}_{4}$ group actions on such handlebodies, up to equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-22T17:15:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M60"
    ],
    "keywords": [
      "equivalence",
      "total number",
      "dimensional handlebodies",
      "algebraic characterization",
      "group actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150906688P"
    }
  }
}