{
  "id": "2107.06000",
  "version": "v1",
  "published": "2021-07-13T11:48:19.000Z",
  "updated": "2021-07-13T11:48:19.000Z",
  "title": "Homotopy types of $\\mathrm{Spin}^c(n)$-gauge groups over $S^4$",
  "authors": [
    "Simon Rea"
  ],
  "comment": "18 pages, submitted to Topology and Its Applications",
  "categories": [
    "math.AT"
  ],
  "abstract": "The gauge group of a principal $G$-bundle $P$ over a space $X$ is the group of $G$-equivariant homeomorphisms of $P$ that cover the identity on $X$. We consider the gauge groups of bundles over $S^4$ with $\\mathrm{Spin}^c(n)$, the complex spin group, as structure group and show how the study of their homotopy types reduces to that of $\\mathrm{Spin}(n)$-gauge groups over $S^4$. We then advance on what is known by providing a partial classification for $\\mathrm{Spin}(7)$- and $\\mathrm{Spin}(8)$-gauge groups over $S^4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-13T11:48:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P15",
      "55Q05"
    ],
    "keywords": [
      "gauge group",
      "complex spin group",
      "homotopy types reduces",
      "equivariant homeomorphisms",
      "structure group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}