Rational string topology

• Autores: Jean-Claude Thomas, Yves Félix , Micheline Vigué-Poirrier
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 9, Nº 1, 2007, págs. 123-156
• Idioma: inglés
• DOI: 10.4171/jems/75
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• Resumen

  • 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.