Rational string topology

Abstract

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