{
  "id": "math/0010310",
  "version": "v3",
  "published": "2000-10-31T01:42:16.000Z",
  "updated": "2001-11-23T20:01:16.000Z",
  "title": "The mapping class group of a genus two surface is linear",
  "authors": [
    "Stephen J. Bigelow",
    "Ryan D. Budney"
  ],
  "comment": "Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-34.abs.html",
  "journal": "Algebr. Geom. Topol. 1 (2001) 699-708",
  "categories": [
    "math.GT",
    "math.AT",
    "math.GR"
  ],
  "abstract": "In this paper we construct a faithful representation of the mapping class group of the genus two surface into a group of matrices over the complex numbers. Our starting point is the Lawrence-Krammer representation of the braid group B_n, which was shown to be faithful by Bigelow and Krammer. We obtain a faithful representation of the mapping class group of the n-punctured sphere by using the close relationship between this group and B_{n-1}. We then extend this to a faithful representation of the mapping class group of the genus two surface, using Birman and Hilden's result that this group is a Z_2 central extension of the mapping class group of the 6-punctured sphere. The resulting representation has dimension sixty-four and will be described explicitly. In closing we will remark on subgroups of mapping class groups which can be shown to be linear using similar techniques.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2001-11-23T20:01:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "57M07",
      "20C15"
    ],
    "keywords": [
      "mapping class group",
      "faithful representation",
      "similar techniques",
      "lawrence-krammer representation",
      "braid group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}