Homologie des espaces de lacets des espaces de configuration

Félix, Yves; Thomas, Jean-Claude

Annales de l'Institut Fourier, Tome 44 (1994) no. 2, pp. 559-568.

Nous calculons dans ce texte l’homologie de l’espace des lacets de l’espace des configurations ordonnées de $k$ points dans une variété compacte simplement connexe $M$.

We compute the loop space homology of the space $F(M,k)$ of configurations of $k$ points in a compact simply connected manifold $M$. We prove in particular that, if $H^{*}(M,\mathbb{Q})$ is not generated by one generator, then the rational homology of $\Omega F(M,k)$ contains a tensor algebra for $k\ge 2$.

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