{
  "id": "2004.04925",
  "version": "v1",
  "published": "2020-04-10T07:09:23.000Z",
  "updated": "2020-04-10T07:09:23.000Z",
  "title": "Homotopy types of gauge groups of $\\mathrm{PU}(p)$-bundles over spheres",
  "authors": [
    "Simon Rea"
  ],
  "comment": "10 pages; Submitted to Topology and Its Applications",
  "categories": [
    "math.AT"
  ],
  "abstract": "We examine the relation between the gauge groups of $\\mathrm{SU}(n)$- and $\\mathrm{PU}(n)$-bundles over $S^{2i}$, with $2\\leq i\\leq n$, particularly when $n$ is a prime. As special cases, for $\\mathrm{PU}(5)$-bundles over $S^4$, we show that there is a rational or $p$-local equivalence $\\mathcal{G}_k\\simeq_{(p)}\\mathcal{G}_l$ for any prime $p$ if, and only if, $(120,k)=(120,l)$, while for $\\mathrm{PU}(3)$-bundles over $S^6$ there is an integral equivalence $\\mathcal{G}_k\\simeq\\mathcal{G}_l$ if, and only if, $(120,k)=(120,l)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-10T07:09:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P15",
      "55Q05"
    ],
    "keywords": [
      "gauge groups",
      "homotopy types",
      "integral equivalence",
      "local equivalence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}