ℤ/pr-hyperbolicity via homology

Abstract

Abstract We show that the homotopy groups of a Moore space P n ( p r ), where p r ≠ 2, are ℤ/ p s -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/ p s -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/ p r -hyperbolic, and deduce some examples.