
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.
55P35, 54N45,55N33,17A65,81T30,17B55, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology
55P35, 54N45,55N33,17A65,81T30,17B55, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology
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