Pure and Applied Mathematics Quarterly

Volume 9 (2013)

Number 1

Special Issue: In Honor of Dennis Sullivan, Part 1 of 2

On the growth of the homology of a free loop space

Pages: 167 – 187

DOI: https://dx.doi.org/10.4310/PAMQ.2013.v9.n1.a4


Yves Félix (Institut de Mathématique, Université Catholique de Louvain, Louvain-La-Neuve, Belgium)

Steve Halperin (Department of Mathematics,University of Maryland, College Park, Md., U.S.A.)

Jean-Claude Thomas (Université d’Angers, France)


We prove that for a wide class of spaces $X$ the homology of the free loop space $H_*(X^{S^1} ; \mathbb{Q})$ 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.


rational homotopy, free loop space homology

Published 31 October 2013