Abstract
We 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.
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Acknowledgements
I would like to thank my PhD supervisor, Stephen Theriault, for many helpful conversations and much encouragement. Changes to the proof of Theorem 1.3 which make the result work for powers of 2 are due to him. I would also like to thank Jie Wu and Ian Leary for their helpful comments.
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Boyde, G. ℤ/pr-hyperbolicity via homology. Isr. J. Math. 260, 141–193 (2024). https://doi.org/10.1007/s11856-023-2563-z
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DOI: https://doi.org/10.1007/s11856-023-2563-z