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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on the category of the free loop space
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by E. Fadell and S. Husseini PDF
Proc. Amer. Math. Soc. 107 (1989), 527-536 Request permission

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
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 107 (1989), 527-536
  • MSC: Primary 55M30; Secondary 55P35, 58E10, 58F05
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0984789-4
  • MathSciNet review: 984789