{
  "id": "math/0109145",
  "version": "v1",
  "published": "2001-09-20T14:16:29.000Z",
  "updated": "2001-09-20T14:16:29.000Z",
  "title": "On the cohomology algebra of free loop spaces",
  "authors": [
    "Bitjong Ndombol",
    "Jean-Claude Thomas"
  ],
  "comment": "21 pages, to appear in Topology",
  "categories": [
    "math.AT",
    "math.AG",
    "math.KT"
  ],
  "abstract": "Let $X$ be a simply connected space and $\\Bbb K$ be any field. The normalized singular cochains $N^*(X; {\\Bbb K})$ admit a natural strongly homotopy commutative algebra structure, which induces a natural product on the Hochschild homology $HH_* N^*X$ of the space $X$. We prove that, endowed with this product, $HH_*N^*X$ is isomorphic to the cohomology algebra of the free loop space of $X$ with coefficients in $\\Bbb K$. We also show how to construct a simpler Hochschild complex which allows direct computation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-09-20T14:16:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57T30",
      "54C35",
      "55S20"
    ],
    "keywords": [
      "free loop space",
      "cohomology algebra",
      "natural strongly homotopy commutative algebra",
      "strongly homotopy commutative algebra structure",
      "simpler hochschild complex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......9145N"
    }
  }
}