{
  "id": "math/0406593",
  "version": "v1",
  "published": "2004-06-29T07:01:42.000Z",
  "updated": "2004-06-29T07:01:42.000Z",
  "title": "Rational String Topology",
  "authors": [
    "Yves Felix",
    "Jean-Claude Thomas",
    "Micheline Vigue-Poirrier"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a 1-connected closed manifold M. We prove that the loop homology of M is isomorphic to the Hochschild cohomology of the commutative graded algebra A_{PL}(M) with coefficients in itself. Some explicit computations of the loop product and the string bracket are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-06-29T07:01:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P35",
      "54N45",
      "55N33",
      "17A65",
      "81T30",
      "17B55"
    ],
    "keywords": [
      "rational string topology",
      "loop product",
      "rational homotopy theory",
      "string bracket",
      "explicit cochain model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6593F"
    }
  }
}