Rational String Topology
Yves Felix, Jean-Claude Thomas, Micheline Vigue-Poirrier
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 commutative graded algebra APL(M) with coefficients in itself. Some explicit computations of the loop product and the string bracket are given.
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