{
  "id": "1310.7302",
  "version": "v2",
  "published": "2013-10-28T03:33:47.000Z",
  "updated": "2015-09-27T02:27:17.000Z",
  "title": "Maximum Orders of Cyclic and Abelian Extendable Actions on Surfaces",
  "authors": [
    "Chao Wang",
    "Yimu Zhang"
  ],
  "comment": "22pages, 10 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $\\Sigma_g (g>1)$ be a closed surface embedded in $S^3$. If a group $G$ can acts on the pair $(S^3, \\Sigma_g)$, then we call such a group action on $\\Sigma_g$ extendable over $S^3$. In this paper we show that the maximum order of extendable cyclic group actions is $4g+4$ when $g$ is even and $4g-4$ when $g$ is odd; the maximum order of extendable abelian group actions is $4g+4$. We also give results of similar questions about extendable group actions over handlebodies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-28T03:33:47.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-09-27T02:27:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M60",
      "57S17",
      "57S25"
    ],
    "keywords": [
      "maximum order",
      "abelian extendable actions",
      "extendable cyclic group actions",
      "extendable abelian group actions",
      "similar questions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.7302W"
    }
  }
}