{
  "id": "1502.02781",
  "version": "v1",
  "published": "2015-02-10T05:14:58.000Z",
  "updated": "2015-02-10T05:14:58.000Z",
  "title": "Infiniteness of $A_\\infty$-types of gauge groups",
  "authors": [
    "Daisuke Kishimoto",
    "Mitsunobu Tsutaya"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let $G$ be a compact connected Lie group and let $P$ be a principal $G$-bundle over $K$. The gauge group of $P$ is the topological group of automorphisms of $P$. For fixed $G$ and $K$, consider all principal $G$-bundles $P$ over $K$. It is proved by Crabb--Sutherland and the second author that the number of $A_n$-types of the gauge groups of $P$ is finite if $n<\\infty$ and $K$ is a finite complex. We show that the number of $A_\\infty$-types of the gauge groups of $P$ is infinite if $K$ is a sphere and there are infinitely many $P$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-10T05:14:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57S05",
      "55P48"
    ],
    "keywords": [
      "gauge group",
      "infiniteness",
      "compact connected lie group",
      "second author",
      "finite complex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150202781K"
    }
  }
}