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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on the category of the free loop space


Authors: E. Fadell and S. Husseini
Journal: Proc. Amer. Math. Soc. 107 (1989), 527-536
MSC: Primary 55M30; Secondary 55P35, 58E10, 58F05
MathSciNet review: 984789
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0984789-4
PII: S 0002-9939(1989)0984789-4
Article copyright: © Copyright 1989 American Mathematical Society