{
  "id": "1210.4664",
  "version": "v3",
  "published": "2012-10-17T08:27:10.000Z",
  "updated": "2015-04-07T21:25:18.000Z",
  "title": "Homotopy transfer and rational models for mapping spaces",
  "authors": [
    "Urtzi Buijs",
    "Javier J. Gutiérrez"
  ],
  "comment": "21 pages. Final version. To appear in J. Homotopy Relat. Struct",
  "categories": [
    "math.AT"
  ],
  "abstract": "By using homotopy transfer techniques in the context of rational homotopy theory, we show that if $C$ is a coalgebra model of a space $X$, then the $A_\\infty$-coalgebra structure in $H_*(X;\\mathbb{Q})\\cong H_*(C)$ induced by the higher Massey coproducts provides the construction of the Quillen minimal model of $X$. We also describe an explicit $L_\\infty$-structure on the complex of linear maps ${\\rm Hom}(H_*(X; \\mathbb{Q}), \\pi_*(\\Omega Y)\\otimes\\mathbb{Q})$, where $X$ is a finite nilpotent CW-complex and $Y$ is a nilpotent CW-complex of finite type, modeling the rational homotopy type of the mapping space ${\\rm map}(X, Y)$. As an application we give conditions on the source and target in order to detect rational $H$-space structures on the components.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-25T08:59:43.000Z",
      "comment": "19 pages. Revised version. Added more examples and corrected some mistakes",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-04-07T21:25:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P62",
      "54C35"
    ],
    "keywords": [
      "mapping space",
      "rational models",
      "higher massey coproducts",
      "rational homotopy theory",
      "rational homotopy type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.4664B"
    }
  }
}