Using integral methods we recover and generalize some results by Félix, Halperin and Thomas on the growth of the rational homology groups of free loop spaces, and obtain a new family of spaces whose -torsion in homotopy groups grows exponentially and satisfies Moore’s Conjecture for all but finitely many primes. In view of the results, we conjecture that there should be a strong connection between exponential growth in the rational homotopy groups and the -torsion homotopy groups for any prime .
En utilisant des méthodes intégrales, nous retrouvons et généralisons certains résultats de Félix, Halperin et Thomas sur la croissance des groupes d’homologie rationnelle des espaces des lacets libres, et obtenons une nouvelle famille d’espaces dont la -torsion dans les groupes d’homotopie croît exponentiellement et satisfait la conjecture de Moore pour tous les nombres premiers, sauf un nombre fini. Au vu des résultats, nous conjecturons qu’il devrait y avoir un lien étroit entre la croissance exponentielle dans les groupes d’homotopie rationnelle et les groupes d’homotopie de -torsion pour tout nombre premier .
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Keywords: Exponential growth, free loop space, homotopy exponent, Moore’s conjecture.
Mot clés : Croissance exponentielle, espace des lacets libre, exposant d’homotopie, conjecture de Moore.
Huang, Ruizhi 1; Theriault, Stephen 2
@article{AIF_2024__74_4_1365_0, author = {Huang, Ruizhi and Theriault, Stephen}, title = {Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups}, journal = {Annales de l'Institut Fourier}, pages = {1365--1382}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {74}, number = {4}, year = {2024}, doi = {10.5802/aif.3627}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3627/} }
TY - JOUR AU - Huang, Ruizhi AU - Theriault, Stephen TI - Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups JO - Annales de l'Institut Fourier PY - 2024 SP - 1365 EP - 1382 VL - 74 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3627/ DO - 10.5802/aif.3627 LA - en ID - AIF_2024__74_4_1365_0 ER -
%0 Journal Article %A Huang, Ruizhi %A Theriault, Stephen %T Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups %J Annales de l'Institut Fourier %D 2024 %P 1365-1382 %V 74 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3627/ %R 10.5802/aif.3627 %G en %F AIF_2024__74_4_1365_0
Huang, Ruizhi; Theriault, Stephen. Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups. Annales de l'Institut Fourier, Volume 74 (2024) no. 4, pp. 1365-1382. doi : 10.5802/aif.3627. https://aif.centre-mersenne.org/articles/10.5802/aif.3627/
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