{
  "id": "1707.07022",
  "version": "v1",
  "published": "2017-07-21T19:02:21.000Z",
  "updated": "2017-07-21T19:02:21.000Z",
  "title": "Homotopy types of gauge groups related to $S^3$-bundles over $S^4$",
  "authors": [
    "Ingrid Membrillo-Solis"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let $M$ be the total space of an $S^3$-bundle over $S^4$ and $G$ be a simply connected simple compact Lie group. If the integral homology of $M$ is torsion free we describe the homotopy type of the gauge groups over $M$ as products of recognisable spaces. For any manifold $M$ with non torsion free homology, we give a $p$-local homotopy decomposition, $p\\geq 5$, of the loop space of the gauge groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-21T19:02:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C35",
      "55P15",
      "55R10",
      "55R25"
    ],
    "keywords": [
      "gauge groups",
      "homotopy type",
      "connected simple compact lie group",
      "non torsion free homology",
      "local homotopy decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}