Rational string topology

  • Yves Félix

    Université Catholique de Louvain, Belgium
  • Jean-Claude Thomas

    Université d'Angers, France
  • Micheline Vigué-Poirrier

    Université de Paris XIII, Villetaneuse, France


We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a 1-connected closed manifold . We prove that the loop homology of is isomorphic to the Hochschild cohomology of the cochain algebra with coefficients in itself. Some explicit computations of the loop product and the string bracket are given.

Cite this article

Yves Félix, Jean-Claude Thomas, Micheline Vigué-Poirrier, Rational string topology. J. Eur. Math. Soc. 9 (2007), no. 1, pp. 123–156

DOI 10.4171/JEMS/75