- Using integral methods we recover and generalize some results by Felix, Halperin and Thomas on the growth of the rational homology groups of free loop spaces, and obtain a new family of spaces whose p-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 p -torsion homotopy groups for any prime p.

- Using integral methods we recover and generalize some results by Felix, Halperin and Thomas on the growth of the rational homology groups of free loop spaces, and obtain a new family of spaces whose p-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 p -torsion homotopy groups for any prime p.

Publication:

Annales de l'Institut Fourier, Tome 74 ( 2024-07-03) no. 4, pp. 1365-1382.

http://dx.doi.org/10.5802/aif.3627

Author:

Ruizhi Huang

Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)

Email：haungrz@amss.ac.cn

Stephen Theriault

School of Mathematics, University of Southampton, Southampton SO17 1BJ (United Kingdom)

Email：s.d.theriault@soton.ac.uk