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.
Original languageEnglish
JournalProceedings of the American Mathematical Society
Volume147
Issue number2
Pages (from-to)897-908
ISSN0002-9939
DOIs
Publication statusPublished - 2019

ID: 212506199