{
  "id": "0903.1470",
  "version": "v2",
  "published": "2009-03-09T01:39:55.000Z",
  "updated": "2010-09-04T04:10:43.000Z",
  "title": "The rational homotopy type of the space of self-equivalences of a fibration",
  "authors": [
    "Yves Felix",
    "Gregory Lupton",
    "Samuel B. Smith"
  ],
  "comment": "27 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let Aut(p) denote the topological monoid of self-fibre-homotopy equivalences of a fibration p:E\\to B. We make a general study of this monoid, especially in rational homotopy theory. When E and B are simply connected CW complexes with E finite, we identify the rational Samelson Lie algebra of the identity component of Aut(p) as the homology of a certain DG Lie algebra of derivations arising from the Koszul-Sullivan model of p. We obtain related identifications for the rational homotopy groups of fibrewise mapping spaces and for the rationalization of a natural nilpotent subgroup of Aut(p).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-09-04T04:10:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P62",
      "55Q15"
    ],
    "keywords": [
      "rational homotopy type",
      "self-equivalences",
      "rational samelson lie algebra",
      "rational homotopy theory",
      "dg lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.1470F"
    }
  }
}