$\mathbb{Z}/p^r$-hyperbolicity via homology

Guy Boyde

Published 2021-06-07Version 1

We show that the homotopy groups of a Moore space $P^n(p^r)$ are $\mathbb{Z}/p^s$-hyperbolic for $s \leq r$ and $p^s \neq 2$. Combined with work of Huang-Wu and Neisendorfer, this completely resolves the question of when such a Moore space is $\mathbb{Z}/p^s$-hyperbolic for $p \geq 5$. We also give a homological criterion for a space to be $\mathbb{Z}/p^r$-hyperbolic, and deduce some examples.