We show that the homotopy groups of a Moore space Pⁿ(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.

中文翻译：

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ℤ/pr-通过同源性的双曲性

我们证明摩尔空间P ⁿ ( p ^r ) 的同伦群（其中p ^r ≠ 2）对于s ≤ r是 ℤ/ p ^s -双曲型。结合 Huang-Wu、Neisendorfer 和 Theriault 的工作，这完全解决了当p ≥ 5时摩尔空间何时为 ℤ/ p ^s -双曲，或者当p = 2 且r ≥ 6 时的问题。我们还给出了空间的普通同调准则是 ℤ/ p ^r -双曲，并推导出一些例子。