{
  "id": "2011.13020",
  "version": "v1",
  "published": "2020-11-25T20:57:51.000Z",
  "updated": "2020-11-25T20:57:51.000Z",
  "title": "From braid groups to mapping class groups",
  "authors": [
    "Lei Chen",
    "Aru Mukherjea"
  ],
  "comment": "25 pages, 3 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we classify homomorphisms from the braid group of $n$ strands to the mapping class group of a genus $g$ surface. In particular, we show that when $g<n-2$, all representations are either cyclic or standard. Our result is sharp in the sense that when $g=n-2$, a generalization of the hyperelliptic representation appears. This gives a classification of genus $g$ surface bundles over the configuration space of the complex plane. As a corollary, we recover partially the result of Aramayona-Souto with a slight improvement, which classifies homomorphisms between mapping class groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-25T20:57:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mapping class group",
      "braid group",
      "hyperelliptic representation appears",
      "configuration space",
      "complex plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}