Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Free loop spaces of finite complexes have infinite category
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by Y. Félix, J. C. Thomas and M. Vigué-Poirrier
Proc. Amer. Math. Soc. 111 (1991), 869-875
DOI: https://doi.org/10.1090/S0002-9939-1991-1025277-8

Abstract:

Let $X$ be a $1$-connected space such that each ${H_i}(X;\mathbb {Z})$ is finitely generated. In this paper we prove that if the reduced homology of $X$ with coefficients in a field is nonzero, then the Lusternik-Schnirelmann category of the free loop space is infinite.
References
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Bibliographic Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 111 (1991), 869-875
  • MSC: Primary 55P50; Secondary 55P62
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1025277-8
  • MathSciNet review: 1025277