{
  "id": "math/0307107",
  "version": "v1",
  "published": "2003-07-09T07:56:57.000Z",
  "updated": "2003-07-09T07:56:57.000Z",
  "title": "Homomorphisms from mapping class groups",
  "authors": [
    "William Harvey",
    "Mustafa Korkmaz"
  ],
  "comment": "11 pages, 2 pictures",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "This paper concerns rigidity of the mapping class groups. We show that any homomorphism $\\phi:{\\rm Mod}_g\\to {\\rm Mod}_h$ between mapping class groups of closed orientable surfaces with distinct genera $g>h$ is trivial if $g\\geq 3$ and has finite image for all $g\\geq 1$. Some implications are drawn for more general homomorphs of these groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-07-09T07:56:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mapping class groups",
      "homomorphism",
      "paper concerns rigidity",
      "distinct genera",
      "finite image"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......7107H"
    }
  }
}