{
  "id": "1005.0681",
  "version": "v2",
  "published": "2010-05-05T07:43:43.000Z",
  "updated": "2011-03-10T12:26:36.000Z",
  "title": "Classification of equivariant vector bundles over two-sphere",
  "authors": [
    "Min Kyu Kim"
  ],
  "comment": "48pages",
  "categories": [
    "math.GR",
    "math.KT",
    "math.RT"
  ],
  "abstract": "We exhaustively classify topological equivariant complex vector bundles over two-sphere under a compact Lie group (not necessarily effective) action. It is shown that inequivariant Chern classes and isotropy representations at (at most) three points are sufficient to classify equivariant vector bundles except a few cases. To do it, we calculate equivariant homotopy of the set of equivariant clutching maps. Holomorphic version of this will be treated in other paper. Classification on two-torus, real projective plane, Klein bottle will appear soon.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-10T12:26:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57S25",
      "55P91",
      "20C99"
    ],
    "keywords": [
      "two-sphere",
      "classification",
      "topological equivariant complex vector bundles",
      "classify topological equivariant complex vector",
      "compact lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.0681K"
    }
  }
}