On the comparison of stable and unstable P-completion
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- On the comparison of stable and unstable P-completion
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In this note we show that a p-complete nilpotent space X has a p-complete suspension spectrum if and only if its homotopy groups pi X-* are bounded p-torsion. In contrast, if pi X-* is not all bounded p-torsion, we locate uncountable rational vector spaces in the integral homology and in the stable homotopy groups of X. To prove this, we establish a homological criterion for p-completeness of connective spectra. Moreover, we illustrate our results by studying the stable homotopy groups of K(Z(p), n) via Goodwillie calculus.
Originalsprog | Engelsk |
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Tidsskrift | Proceedings of the American Mathematical Society |
Vol/bind | 147 |
Udgave nummer | 2 |
Sider (fra-til) | 897-908 |
ISSN | 0002-9939 |
DOI | |
Status | Udgivet - 2019 |
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