{
  "id": "0902.4876",
  "version": "v1",
  "published": "2009-02-27T17:29:40.000Z",
  "updated": "2009-02-27T17:29:40.000Z",
  "title": "A rational splitting of a based mapping space",
  "authors": [
    "Katsuhiko Kuribayashi",
    "Toshihiro Yamaguchi"
  ],
  "comment": "This is the version published by Algebraic & Geometric Topology on 7 March 2006",
  "journal": "Algebr. Geom. Topol. 6 (2006) 309-327",
  "doi": "10.2140/agt.2006.6.309",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let F_*(X, Y) be the space of base-point-preserving maps from a connected finite CW complex X to a connected space Y. Consider a CW complex of the form X cup_{alpha}e^{k+1} and a space Y whose connectivity exceeds the dimension of the adjunction space. Using a Quillen-Sullivan mixed type model for a based mapping space, we prove that, if the bracket length of the attaching map alpha: S^k --> X is greater than the Whitehead length WL(Y) of Y, then F_*(X cup_{alpha}e^{k+1}, Y) has the rational homotopy type of the product space F_*(X, Y) times Omega^{k+1}Y. This result yields that if the bracket lengths of all the attaching maps constructing a finite CW complex X are greater than WL(Y) and the connectivity of Y is greater than or equal to dim X, then the mapping space F_*(X, Y) can be decomposed rationally as the product of iterated loop spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-27T17:29:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P62",
      "54C35"
    ],
    "keywords": [
      "mapping space",
      "rational splitting",
      "bracket length",
      "connected finite cw complex",
      "quillen-sullivan mixed type model"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.4876K"
    }
  }
}