A note on the category of the free loop space. (English) Zbl 0676.58019

Fadell, E.; Husseini, S.

Proc. Am. Math. Soc. 107, No. 2, 527-536 (1989).

Summary: A useful result in critical point theory is that the Lyusternik- Schnirelmann 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.

MSC:

58E05	Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
55P35	Loop spaces
55R20	Spectral sequences and homology of fiber spaces in algebraic topology

Keywords:

critical point theory; Lyusternik-Schnirelmann category; based loops; free loops

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