{
  "id": "1109.6479",
  "version": "v3",
  "published": "2011-09-29T11:15:23.000Z",
  "updated": "2012-10-21T06:54:28.000Z",
  "title": "Groupoid-theoretical methods in the mapping class groups of surfaces",
  "authors": [
    "Nariya Kawazumi",
    "Yusuke Kuno"
  ],
  "comment": "43 pages, 7 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We provide some language for algebraic study of the mapping class groups for surfaces with non-connected boundary. As applications, we generalize our previous results on Dehn twists to any compact connected oriented surfaces with non-empty boundary. Moreover we embed the `smallest' Torelli group in the sense of Putman into a pro-nilpotent group coming from the Goldman Lie algebra. The graded quotients of the embedding equal the Johnson homomorphisms of all degrees if the boundary is connected.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-10-21T06:54:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N05",
      "20F34",
      "32G15"
    ],
    "keywords": [
      "mapping class groups",
      "groupoid-theoretical methods",
      "goldman lie algebra",
      "dehn twists",
      "non-empty boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.6479K"
    }
  }
}