no. 6
On The Growth of the Homology of a Free Loop Space II
[Sur la croissance de l’homologie des espaces de lacets II]
Félix, Yves1 ; Halperin, Steve2 ; Thomas, Jean-Claude3
1 Université Catholique de Louvain, Institut de Mathématique, 2, Chemin du cyclotron, 1348 Louvain-La-Neuve (Belgium)
2 University of Maryland, Department of Mathematics, Mathematics Building, College Park, MD 20742 (USA)
3 Université d’Angers, LAREMA, 2 Bd Lavoisier, 49045 Angers Cedex (France)
Annales de l'Institut Fourier, Tome 67 (2017) no. 6, pp. 2519-2531.

Controlled exponential growth is a stronger version of exponential growth. We prove that the homology of the free loop space ℒX has controlled exponential growth in two important situations : (1) when X is a connected sum of manifolds whose rational cohomologies are not monogenic, (2) when the rational homotopy Lie algebra L X contains an inert element and ρ(L X )<ρ(L X /[L X ,L X ]), where ρ(V) denotes the radius of convergence of V.

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 X ont une croissance exponentielle controlée dans deux cas : lorsque X est la somme connexe de variétés dont la cohomologie n’est pas monogène, et lorsque l’algèbre de Lie L X a une croissance exponentielle strictement plus grande que ses indécomposables.

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Révisé le :
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DOI : 10.5802/aif.3141
Classification : 55P62
Keywords: free loop space, exponential growth, inert attachment
Mots-clés : espace des lacets libres, croissance exponentielle, attachement inerte

Félix, Yves 1 ; Halperin, Steve 2 ; Thomas, Jean-Claude 3

1 Université Catholique de Louvain, Institut de Mathématique, 2, Chemin du cyclotron, 1348 Louvain-La-Neuve (Belgium)
2 University of Maryland, Department of Mathematics, Mathematics Building, College Park, MD 20742 (USA)
3 Université d’Angers, LAREMA, 2 Bd Lavoisier, 49045 Angers Cedex (France)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Félix, Yves; Halperin, Steve; Thomas, Jean-Claude. On The Growth of the Homology of a Free Loop Space II. Annales de l'Institut Fourier, Tome 67 (2017) no. 6, pp. 2519-2531. doi : 10.5802/aif.3141. https://aif.centre-mersenne.org/articles/10.5802/aif.3141/

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