Geodesic
Rational string topology
Journal of the European Mathematical Society, Tome 9 (2007) no. 1, pp. 123-156.

Voir la notice de l'article provenant de la source EMS Press

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∗(M) with coefficients in itself. Some explicit computations of the loop product and the string bracket are given.
DOI : 10.4171/jems/75
Classification : 55-XX, 17-XX, 54-XX, 81-XX
Keywords: String homology, rational homotopy, Hochschild cohomology, free loop space, loop space homology 
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Yves Félix; Jean-Claude Thomas; Micheline Vigué-Poirrier. Rational string topology. Journal of the European Mathematical Society, Tome 9 (2007) no. 1, pp. 123-156. doi : 10.4171/jems/75. http://geodesic.mathdoc.fr/articles/10.4171/jems/75/

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