Free loop spaces of finite complexes have infinite category

Félix, Y.; Thomas, J. C.; Vigué-Poirrier, M.

doi:10.1090/S0002-9939-1991-1025277-8

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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 be a -connected space such that each ${H_i}(X;\mathbb{Z})$ is finitely generated. In this paper we prove that if the reduced homology of with coefficients in a field is nonzero, then the Lusternik-Schnirelmann category of the free loop space is infinite.

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