{
  "id": "0705.0144",
  "version": "v1",
  "published": "2007-05-01T17:18:32.000Z",
  "updated": "2007-05-01T17:18:32.000Z",
  "title": "Formality of function spaces",
  "authors": [
    "Micheline Vigué-Poirrier"
  ],
  "comment": "8 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let $X$ be a nilpotent space such that there exists $p\\geq 1$ with $H^p(X,\\mathbb Q) \\ne 0$ and $H^n(X,\\mathbb Q)=0$ if $n>p$. Let $Y$ be a m-connected space with $m\\geq p+1$ and $H^*(Y,\\mathbb Q)$ is finitely generated as algebra. We assume that $X$ is formal and there exists $p$ odd such that $H^p(X,\\mathbb Q) \\ne 0$. We prove that if the space $\\mathcal F(X,Y)$ of continuous maps from $X$ to $Y$ is formal, then $Y$ has the rational homotopy type of a product of Eilenberg Mac Lane spaces. At the opposite, we exhibit an example of a 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": "2007-05-01T17:18:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P62",
      "55P35"
    ],
    "keywords": [
      "function spaces",
      "eilenberg mac lane spaces",
      "rational homotopy type",
      "nilpotent space",
      "formal space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.0144V"
    }
  }
}