{
  "id": "1603.08100",
  "version": "v1",
  "published": "2016-03-26T11:08:23.000Z",
  "updated": "2016-03-26T11:08:23.000Z",
  "title": "The rational homology ring of the based loop space of the gauge groups and the spaces of connections on a four-manifold",
  "authors": [
    "Svjetlana Terzic"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "We provide the rational-homotopic proof that the ranks of the homotopy groups of a simply connected four-manifold depend only on its second Betti number. We also consider the based loop spaces of the gauge groups and the spaces of connections of a simply connected four-manifold and, appealing to~\\cite{TI} and using the models from the rational homotopy theory, we obtain the explicit formulas for their rational Pontrjagin homology rings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-26T11:08:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P62",
      "55P35",
      "57R19",
      "81T13"
    ],
    "keywords": [
      "loop space",
      "rational homology ring",
      "gauge groups",
      "connections",
      "rational pontrjagin homology rings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}