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


Free loop spaces of finite complexes have infinite category

Authors: Y. Félix, J. C. Thomas and M. Vigué-Poirrier
Journal: Proc. Amer. Math. Soc. 111 (1991), 869-875
MSC: Primary 55P50; Secondary 55P62
MathSciNet review: 1025277
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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.

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PII: S 0002-9939(1991)1025277-8
Article copyright: © Copyright 1991 American Mathematical Society