Controlled exponential growth is a stronger version of exponential growth. We prove that the homology of the free loop space has controlled exponential growth in two important situations : (1) when is a connected sum of manifolds whose rational cohomologies are not monogenic, (2) when the rational homotopy Lie algebra contains an inert element and , where denotes the radius of convergence of .
La croissance exponentielle controlée est une version forte de la croissance exponentielle. Nous prouvons que les nombres de Betti de l’espace des lacets libres sur un espace ont une croissance exponentielle controlée dans deux cas : lorsque est la somme connexe de variétés dont la cohomologie n’est pas monogène, et lorsque l’algèbre de Lie a une croissance exponentielle strictement plus grande que ses indécomposables.
Revised : 2017-05-27
Accepted : 2017-08-07
Published online : 2017-12-14
DOI : https://doi.org/10.5802/aif.3141
Classification: 55P62
Keywords: free loop space, exponential growth, inert attachment
@article{AIF_2017__67_6_2519_0,
author = {F\'elix, Yves and Halperin, Steve and Thomas, Jean-Claude},
title = {On The Growth of the Homology of a Free Loop Space II},
journal = {Annales de l'Institut Fourier},
publisher = {Association des Annales de l'institut Fourier},
volume = {67},
number = {6},
year = {2017},
pages = {2519-2531},
doi = {10.5802/aif.3141},
language = {en},
url = {aif.centre-mersenne.org/item/AIF_2017__67_6_2519_0}
}
Félix, Yves; Halperin, Steve; Thomas, Jean-Claude. On The Growth of the Homology of a Free Loop Space II. Annales de l'Institut Fourier, Volume 67 (2017) no. 6, pp. 2519-2531. doi : 10.5802/aif.3141. https://aif.centre-mersenne.org/item/AIF_2017__67_6_2519_0/
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