{
  "id": "1804.01732",
  "version": "v2",
  "published": "2018-04-05T08:31:35.000Z",
  "updated": "2018-07-18T13:53:29.000Z",
  "title": "On the Continuous Cohomology of a semi-direct product Lie group",
  "authors": [
    "Naoya Suzuki"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let $G$ be a Lie group and $H$ be a subgroup of it. We can construct a bisimplicial manifold $NG(*) \\rtimes NH(*)$ and the de Rham complex $\\Omega^*(NG(*) \\rtimes NH(*))$ on it. This complex is a triple complex and the cohomology of its total complex is isomorphic to $H^*(B(G \\rtimes H))$. In this paper, we show that the total complex of the double complex $\\Omega^q(NG(*) \\rtimes NH(*))$ is isomorphic to the continuous cohomology $H_c^*(G \\rtimes H;S^q{\\mathcal G} \\times S^q{\\mathcal H})$ for any fixed $q$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2018-07-18T13:53:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semi-direct product lie group",
      "continuous cohomology",
      "total complex",
      "rham complex",
      "triple complex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}