Yves Felix, Jean-Claude Thomas, Micheline Vigue-Poirrier
Published 2004-06-29Version 1
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 A_{PL}(M) with coefficients in itself. Some explicit computations of the loop product and the string bracket are given.
A reduction of the string bracket to the loop product
Loop homology algebra of a closed manifold
The Milnor-Moore theorem for $L_\infty$ algebras in rational homotopy theory
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