{
  "id": "1705.07937",
  "version": "v1",
  "published": "2017-05-22T18:26:30.000Z",
  "updated": "2017-05-22T18:26:30.000Z",
  "title": "On the cohomology of the mapping class group of the punctured projective plane",
  "authors": [
    "Miguel A. Maldonado",
    "Miguel A. Xicoténcatl"
  ],
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "The mapping class group $\\Gamma^k(N_g)$ of a non-orientable surface with punctures is studied via classical homotopy theory of configuration spaces. In particular, we obtain a non-orientable version of the Birman exact sequence. In the case of $\\mathbb R {\\rm P}^2$, we analize the Serre spectral sequence of a fiber bundle $F_k(\\mathbb R {\\rm P}^2)/\\Sigma_k \\to X_k \\to BSO(3)$ where $X_k$ is a $K(\\Gamma^k(\\mathbb R {\\rm P}^2),1)$ and $F_k(\\mathbb R {\\rm P}^2)/\\Sigma_k$ denotes the configuration space of unordered $k$-tuples of distinct points in $\\mathbb R {\\rm P}^2$. As a consequence, we express the mod-2 cohomology of $\\Gamma^k(\\mathbb R {\\rm P}^2)$ in terms of that of $F_k(\\mathbb R {\\rm P}^2)/\\Sigma_k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-22T18:26:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mapping class group",
      "punctured projective plane",
      "cohomology",
      "configuration space",
      "serre spectral sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}