Geodesic
Some asymptotic formulae for torsion in homotopy groups
Canadian journal of mathematics, Tome 76 (2024) no. 4, pp. 1339-1357

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DOI

Inspired by a remarkable work of Félix, Halperin, and Thomas on the asymptotic estimation of the ranks of rational homotopy groups, and more recent works of Wu and the authors on local hyperbolicity, we prove two asymptotic formulae for torsion rank of homotopy groups, one using ordinary homology and one using K-theory. We use these to obtain explicit quantitative asymptotic lower bounds on the torsion rank of the homotopy groups for many interesting spaces after suspension, including Moore spaces, Eilenberg–MacLane spaces, complex projective spaces, complex Grassmannians, Milnor hypersurfaces, and unitary groups.
DOI : 10.4153/S0008414X2300041X
Mots-clés : Homotopy growth, unstable, torsion, hyperbolicity 
Boyde, Guy; Huang, Ruizhi. Some asymptotic formulae for torsion in homotopy groups. Canadian journal of mathematics, Tome 76 (2024) no. 4, pp. 1339-1357. doi: 10.4153/S0008414X2300041X
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