{
  "id": "1810.04771",
  "version": "v1",
  "published": "2018-10-10T23:04:49.000Z",
  "updated": "2018-10-10T23:04:49.000Z",
  "title": "The mod-$p$ homology of the classifying spaces of certain gauge groups",
  "authors": [
    "Daisuke Kishimoto",
    "Stephen Theriault"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let $G$ be a simply-connected, simple compact Lie group of type $\\{n_{1},\\ldots,n_{\\ell}\\}$, where $n_{1}<\\cdots <n_{\\ell}$. Let $\\mathcal{G}_k$ be the gauge group of the principal $G$-bundle (namedright{P}{}{S^{4}}) whose isomorphism class is determined by the the second Chern class having value $k\\in\\mathbb{Z}$. We calculate the mod-$p$ homology of the classifying space $B\\mathcal{G}_k$ provided that $n_{\\ell}<p-1$ and $p$ does not divide $k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-10T23:04:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R40",
      "81T13"
    ],
    "keywords": [
      "gauge group",
      "classifying space",
      "simple compact lie group",
      "isomorphism class",
      "second chern class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}