A note on the category of the free loop space

Fadell, E.; Husseini, S.

doi:10.1090/S0002-9939-1989-0984789-4

A note on the category of the free loop space
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by E. Fadell and S. Husseini

Proc. Amer. Math. Soc. 107 (1989), 527-536

DOI: https://doi.org/10.1090/S0002-9939-1989-0984789-4

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Abstract:

A useful result in critical point theory is that the LjusternikSchnirelmann category of the space of based loops on a compact simply connected manifold $M$ is infinite (because the cup length of $M$ is infinite). However, the space of free loops on $M$ may have trivial products. This note shows that, nevertheless, the space of the free loops also has infinite category.

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