On the comparison of stable and unstable P-completion
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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On the comparison of stable and unstable P-completion. / Barthel, Tobias; Bousfield, A. K.
I: Proceedings of the American Mathematical Society, Bind 147, Nr. 2, 2019, s. 897-908.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - On the comparison of stable and unstable P-completion
AU - Barthel, Tobias
AU - Bousfield, A. K.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
U2 - 10.1090/proc/14250
DO - 10.1090/proc/14250
M3 - Journal article
VL - 147
SP - 897
EP - 908
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 2
ER -
ID: 212506199