Let $M$ be a 1-connected closed manifold of dimension $m$ and $LM$ be the space of free loops on $M$. M.Chas and D.Sullivan defined a structure of BV-algebra on the singular homology of $LM$, $H_{*}(LM;k)$. When the ring of coefficients is a field of characteristic zero, we prove that there exists a BV-algebra structure on the Hochschild cohomology $H{H}^{*}(C^{*}\left(M\right);C^{*}\left(M\right))$ which extends the canonical structure of Gerstenhaber algebra. We construct then an isomorphism of BV-algebras between $H{H}^{*}(C^{*}\left(M\right);C^{*}\left(M\right))$ and the shifted homology $H_{*+m}(LM;k)$. We also prove that the...

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 $C^{*}\left(M\right)$ with coefficients in $C^{*}\left(M\right)$. Some explicit computations of the loop product and the string bracket are given.