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 simply connected closed manifold M. We prove that the loop homology of M is isomorphic to the Hochschild cohomology of the cochain algebra C*(M) with coefficients in C*(M). Some explicit computations of the loop product and the string bracket are given. © European Mathematical Society 2007.