On the growth of the homology of a free loop space

Félix, Yves;Halperin, Steve;Thomas, Jean-Claude
(2013) Pure and Applied Mathematics Quarterly — Vol. 9, p. 167-187 (2013)

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  • Félix, YvesUCLouvain
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  • Halperin, Steve
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  • Thomas, Jean-Claude
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Abstract
We prove that for a wide class of spaces X the homology of the free loop space H∗(XS1;Q) has a very strong exponential growth. We call this convergence, controlled exponential growth, and we prove the good behavior of the controlled exponential growth with respect to fibrations.
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Félix, Y., Halperin, S., & Thomas, J.-C. (2013). On the growth of the homology of a free loop space. Pure and Applied Mathematics Quarterly, 9, 167-187. https://doi.org/10.4310/PAMQ.2013.v9.n1.a4 (Original work published 2013)