{
  "id": "math/0203137",
  "version": "v2",
  "published": "2002-03-14T17:31:57.000Z",
  "updated": "2003-06-27T15:42:08.000Z",
  "title": "Loop homology algebra of a closed manifold",
  "authors": [
    "Yves Félix",
    "Jean-Claude Thomas",
    "Micheline Vigué-Poirrier"
  ],
  "comment": "New version 19 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "The loop homology of a closed orientable manifold $M$ of dimension $d$ is the ordinary homology of the free loop space $M^{S^1}$ with degrees shifted by $d$, i.e. $\\mathbb H_*(M^{S^1}) = H_{*+d}(M^{S^1})$. Chas and Sullivan have defined a loop product on $\\mathbb H_*(M^{S^1})$ and an intersection morphism $I : \\mathbb H_*(M^{S^1}) \\to H_*(\\Omega M)$. The algebra $\\mathbb H_*(M^{S^1})$ is commutative and $I$ is a morphism of algebras. In this paper we produce a model that computes the algebra $\\mathbb H_*(M^{S^1})$ and the morphism $I$. We show that the kernel of $I$ is nilpotent and that the image is contained in the center of $H_*(\\Omega M)$, which is in general quite small.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-06-27T15:42:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P35",
      "54N45",
      "55N33",
      "17A65",
      "81T30",
      "17B55"
    ],
    "keywords": [
      "loop homology algebra",
      "closed manifold",
      "free loop space",
      "general quite small",
      "loop product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......3137F"
    }
  }
}