{
  "id": "1901.08028",
  "version": "v1",
  "published": "2019-01-23T18:02:36.000Z",
  "updated": "2019-01-23T18:02:36.000Z",
  "title": "Braid groups, mapping class groups and their homology with twisted coefficients",
  "authors": [
    "Andrea Bianchi"
  ],
  "comment": "17 pages, 3 figures",
  "categories": [
    "math.AT"
  ],
  "abstract": "We consider the Birman-Hilden inclusion $\\varphi\\colon\\mathfrak{Br}_{2g+1}\\to\\Gamma_{g,1}$ of the braid group into the mapping class group of an orientable surface with boundary, and prove that $\\varphi$ is stably trivial in homology with twisted coefficients in the symplectic representation $H_1(\\Sigma_{g,1})$ of the mapping class group; this generalises a result of Song and Tillmann regarding homology with constant coefficients. Furthermore we show that the stable homology of the braid group with coefficients in $\\varphi^*(H_1(\\Sigma_{g,1}))$ has only $4$-torsion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-23T18:02:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "55N25",
      "55R20",
      "55R35",
      "55R37",
      "55R40",
      "55R80"
    ],
    "keywords": [
      "mapping class group",
      "braid group",
      "twisted coefficients",
      "birman-hilden inclusion",
      "symplectic representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}