{
  "id": "math/0607600",
  "version": "v1",
  "published": "2006-07-24T15:52:54.000Z",
  "updated": "2006-07-24T15:52:54.000Z",
  "title": "Measure equivalence rigidity of the mapping class group",
  "authors": [
    "Yoshikata Kida"
  ],
  "comment": "39 pages",
  "journal": "Ann.of Math.(2) 171 (2010) 1851-1901",
  "doi": "10.4007/annals.2010.171.1851",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We show that the mapping class group of a compact orientable surface with higher complexity has the following extreme rigidity in the sense of measure equivalence: if the mapping class group is measure equivalent to a discrete group, then they are commensurable up to finite kernel. Moreover, we describe all lattice embeddings of the mapping class group into a locally compact second countable group. We also obtain similar results for finite direct products of mapping class groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-07-24T15:52:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F38",
      "37A20"
    ],
    "keywords": [
      "mapping class group",
      "measure equivalence rigidity",
      "finite direct products",
      "locally compact second countable group",
      "extreme rigidity"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7600K"
    }
  }
}