{
  "id": "1608.02400",
  "version": "v1",
  "published": "2016-08-08T12:16:47.000Z",
  "updated": "2016-08-08T12:16:47.000Z",
  "title": "On connections on principal bundles",
  "authors": [
    "Indranil Biswas"
  ],
  "comment": "Final version",
  "categories": [
    "math.DG"
  ],
  "abstract": "A new construction of a universal connection was given in \\cite{BHS}. The main aim here is to explain this construction. A theorem of Atiyah and Weil says that a holomorphic vector bundle $E$ over a compact Riemann surface admits a holomorphic connection if and only if the degree of every direct summand of $E$ is degree. In \\cite{AB}, this criterion was generalized to principal bundles on compact Riemann surfaces. This criterion for principal bundles is also explained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-08T12:16:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C05",
      "53C07",
      "32L05"
    ],
    "keywords": [
      "principal bundles",
      "compact riemann surface admits",
      "holomorphic vector bundle",
      "construction",
      "direct summand"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}