The cohomology algebra of certain free loop spaces

Volume 154 / 1997

Katsuhiko Kuribayashi, Toshihiro Yamaguchi Fundamenta Mathematicae 154 (1997), 57-73 DOI: 10.4064/fm-154-1-57-73


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.


  • Katsuhiko Kuribayashi
  • Toshihiro Yamaguchi

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