{
  "id": "1903.06065",
  "version": "v1",
  "published": "2019-03-14T15:12:42.000Z",
  "updated": "2019-03-14T15:12:42.000Z",
  "title": "Splitting of the homology of the punctured mapping class group",
  "authors": [
    "Andrea Bianchi"
  ],
  "comment": "30 pages, 16 figures",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let $\\Gamma_{g,1}^m$ be the mapping class group of the orientable surface $\\Sigma_{g,1}^m$ of genus $g$ with one parametrised boundary curve and $m$ permutable punctures; when $m=0$ we omit it from the notation. Let $\\beta_{m}(\\Sigma_{g,1})$ be the braid group on $m$ strands of the surface $\\Sigma_{g,1}$. We prove that $H_*(\\Gamma_{g,1}^m;\\mathbb{Z}_2)\\cong H_*(\\Gamma_{g,1};H_*(\\beta_{m}(\\Sigma_{g,1});\\mathbb{Z}_2))$. The main ingredient is the computation of $H_*(\\beta_{m}(\\Sigma_{g,1});\\mathbb{Z}_2)$ as a symplectic representation of $\\Gamma_{g,1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-14T15:12:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "55N25",
      "55R20",
      "55R35",
      "55R40",
      "55R80",
      "55T10"
    ],
    "keywords": [
      "punctured mapping class group",
      "parametrised boundary curve",
      "braid group",
      "main ingredient",
      "symplectic representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}