Exponential growth of homotopy groups of suspended finite complexes

Abstract

We study the asymptotic behavior of the homotopy groups of simply connected finite $p$-local complexes, and define a space to be locally hyperbolic if its homotopy groups have exponential growth. Under some certain conditions related to the functorial decomposition of loop suspension, we prove that the suspended finite complexes are locally hyperbolic if suitable but accessible information of the homotopy groups is known. In particular, we prove that Moore spaces are locally hyperbolic, and other candidates are also given.

To appear in Mathematische Zeitschrift

Cited by in corpus (2)

• Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups
• Some asymptotic formulae for torsion in homotopy groups