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.

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.

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.

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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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