Geodesic
The cohomology algebra of certain free loop spaces
Fundamenta Mathematicae, Tome 154 (1997) no. 1, pp. 57-73

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $X$ be a simply connected space and $LX$ the space of free loops on $X$. We determine the mod $p$ cohomology algebra of $LX$ when the mod p cohomology of $X$ is generated by one element or is an exterior algebra on two generators. We also provide lower bounds on the dimensions of the Hodge decomposition factors of the rational cohomology of $LX$ when the rational cohomology of $X$ is a graded complete intersection algebra. The key to both of these results is the identification of an important subalgebra of the Hochschild homology of a graded complete intersection algebra over a field.
DOI : 10.4064/fm-154-1-57-73

Katsuhiko Kuribayashi 1 ; Toshihiro Yamaguchi 1

1 
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Katsuhiko Kuribayashi; Toshihiro Yamaguchi. The cohomology algebra of certain free loop spaces. Fundamenta Mathematicae, Tome 154 (1997) no. 1, pp. 57-73. doi: 10.4064/fm-154-1-57-73

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