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. 123–156DOI 10.4171/JEMS/75