{
  "id": "0708.3261",
  "version": "v1",
  "published": "2007-08-23T23:41:07.000Z",
  "updated": "2007-08-23T23:41:07.000Z",
  "title": "Complex Structures on Principal Bundles",
  "authors": [
    "Martin Laubinger"
  ],
  "comment": "17 pages",
  "categories": [
    "math.DG",
    "math.CV"
  ],
  "abstract": "Holomorphic principal G-bundles over a complex manifold M can be studied using non-abelian cohomology groups H^1(M,G). On the other hand, if M=\\Sigma is a closed Riemann surface, there is a correspondence between holomorphic principal G-bundles over \\Sigma and coadjoint orbits in the dual of a central extension of the Lie algebra C^\\infty(\\Sigma, \\g). We review these results and provide the details of an integrability condition for almost complex structures on smoothly trivial bundles. This article is a shortened version of the author's Diplom thesis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-23T23:41:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58D27",
      "81R10",
      "32Q60"
    ],
    "keywords": [
      "complex structures",
      "principal bundles",
      "holomorphic principal g-bundles",
      "authors diplom thesis",
      "non-abelian cohomology groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.3261L"
    }
  }
}