{
  "id": "1808.08248",
  "version": "v1",
  "published": "2018-08-24T18:08:57.000Z",
  "updated": "2018-08-24T18:08:57.000Z",
  "title": "On the non-realizability of braid groups by homeomorphisms",
  "authors": [
    "Lei Chen"
  ],
  "comment": "8 pages, 3 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we will show that the projection $\\text{Homeo}^+(D^2_n)\\to B_n$ does not have a section; i.e. the braid group $B_n$ cannot be geometrically realized as a group of homeomorphisms of a disk fixing the boundary point-wise and $n$ marked points in the interior as a set. We also give a new proof of a result of Markovic that the mapping class group of a closed surface cannot be geometrically realized as a group of homeomorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-24T18:08:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "braid group",
      "homeomorphisms",
      "non-realizability",
      "mapping class group",
      "marked points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}