On The Growth of the Homology of a Free Loop Space II
[Sur la croissance de l’homologie des espaces de lacets II]
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 X 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 : https://doi.org/10.5802/aif.3141
Classification : 55P62
Mots clés : espace des lacets libres, croissance exponentielle, attachement inerte
@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},
     pages = {2519--2531},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {67},
     number = {6},
     year = {2017},
     doi = {10.5802/aif.3141},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3141/}
}
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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