JournalsjemsVol. 9, No. 1pp. 123–156

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
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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 MM. We prove that the loop homology of MM is isomorphic to the Hochschild cohomology of the cochain algebra C(M)C^\ast(M) with coefficients in itself. Some explicit computations of the loop product and the string bracket are given.

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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