{
  "id": "1110.6145",
  "version": "v2",
  "published": "2011-10-27T17:37:58.000Z",
  "updated": "2015-08-01T14:48:56.000Z",
  "title": "Rational homotopy theory of mapping spaces via Lie theory for L-infinity algebras",
  "authors": [
    "Alexander Berglund"
  ],
  "comment": "25 pages. Final version to appear in Homology, Homotopy and Applications",
  "categories": [
    "math.AT"
  ],
  "abstract": "We calculate the higher homotopy groups of the Deligne-Getzler infinity-groupoid associated to a nilpotent L-infinity algebra. As an application, we present a new approach to the rational homotopy theory of mapping spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-27T17:37:58.000Z",
      "abstract": "We calculate the higher homotopy groups of the Deligne-Getzler infinity-groupoid associated to an L-infinity algebra and we describe Sullivan models for its connected components. As an application, we present a new approach to the rational homotopy theory of mapping spaces. For a connected space X and a nilpotent space Y of finite type, the mapping space Map(X,Y_Q) is homotopy equivalent to the infinity-groupoid associated to the completed tensor product of A and L, where A is a commutative differential graded algebra model for X and L is an L-infinity algebra model for Y. This enables us to calculate Sullivan models for the components of Map(X,Y_Q).",
      "comment": "21 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-08-01T14:48:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P62",
      "55U10"
    ],
    "keywords": [
      "rational homotopy theory",
      "mapping space",
      "lie theory",
      "sullivan models",
      "l-infinity algebra model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.6145B"
    }
  }
}