ℤ/pr-hyperbolicity via homology

Abstract

AbstractWe show that the homotopy groups of a Moore space Pn(pr), where pr ≠ 2, are ℤ/ps-hyperbolic for s ≤ r. Combined with work of Huang–Wu, Neisendorfer, and Theriault, this completely resolves the question of when such a Moore space is ℤ/ps-hyperbolic for p ≥ 5, or when p = 2 and r ≥ 6. We also give a criterion in ordinary homology for a space to be ℤ/pr-hyperbolic, and deduce some examples.