{
  "id": "1401.2215",
  "version": "v2",
  "published": "2014-01-10T01:47:39.000Z",
  "updated": "2014-01-21T01:58:28.000Z",
  "title": "The group fixed by a family of endomorphisms of a surface group",
  "authors": [
    "Jianchun Wu",
    "Qiang Zhang"
  ],
  "comment": "16 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "For a closed surface $S$ with $\\chi(S)<0$, we show that the fixed subgroup of a family $\\mathcal B$ of endomorphisms of $\\pi_1(S)$ has $\\rk \\fix\\mathcal B\\leq \\rk \\pi_1(S)$. In particular, if $\\mathcal B$ contains a non-epimorphic endomorphism, then $\\rk \\fix\\mathcal B\\leq \\frac{1}{2} \\rk \\pi_1(S)$. We also show that geometric subgroups of $\\pi_1(S)$ are inert, and hence the fixed subgroup of a family of epimorphisms of $\\pi_1(S)$ is also inert.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-21T01:58:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M07",
      "20F34",
      "55M20"
    ],
    "keywords": [
      "surface group",
      "fixed subgroup",
      "non-epimorphic endomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.2215W"
    }
  }
}