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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
DOI: https://doi.org/10.1090/S0002-9939-1991-1025277-8
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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DOI: https://doi.org/10.1090/S0002-9939-1991-1025277-8
Article copyright: © Copyright 1991 American Mathematical Society

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