{
  "id": "0706.2977",
  "version": "v1",
  "published": "2007-06-20T12:10:07.000Z",
  "updated": "2007-06-20T12:10:07.000Z",
  "title": "Rational formality of function spaces",
  "authors": [
    "Micheline Vigue-Poirrier"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let $X$ be a nilpotent space such that there exists $N\\geq 1$ with $H^N(X,\\mathbb Q) \\ne 0$ and $H^n(X,\\mathbb Q)=0$ if $n>N$. Let $Y$ be a m-connected space with $m\\geq N+1$ and $H^*(Y,\\mathbb Q)$ is finitely generated as algebra. We assume that the odd part of the rational Hurewicz homomorphism: $\\pi_{odd}(X)\\otimes \\mathbb Q\\to H_{odd}(X,\\mathbb Q)$ is non-zero. We prove that if the space $\\mathcal F(X,Y)$ of continuous maps from $X$ to $Y$ is rationally formal, then $Y$ has the rational homotopy type of a finite product of Eilenberg Mac Lane spaces. At the opposite, we exhibit an example of a rationally formal space $\\mathcal F(S^2,Y)$ where $Y$ is not rationally equivalent to a product of Eilenberg Mac Lane spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-20T12:10:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P62",
      "55P35"
    ],
    "keywords": [
      "function spaces",
      "rational formality",
      "eilenberg mac lane spaces",
      "rational hurewicz homomorphism",
      "rational homotopy type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.2977V"
    }
  }
}