Geodesic
Rational string topology
Journal of the European Mathematical Society, Tome 9 (2007) no. 1, pp. 123-156
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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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     title = {Rational string topology},
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     pages = {123--156},
     year = {2007},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/75/}
}
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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

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