On the comparison of stable and unstable P-completion

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Tobias Barthel, A. K. Bousfield

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.
TidsskriftProceedings of the American Mathematical Society
Sider (fra-til)897-908
StatusUdgivet - 2019

ID: 212506199