On the comparison of stable and unstable P-completion

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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 tidsskriftTidsskriftartikelForskningfagfællebedømt

Harvard

Barthel, T & Bousfield, AK 2019, 'On the comparison of stable and unstable P-completion' Proceedings of the American Mathematical Society, bind 147, nr. 2, s. 897-908. https://doi.org/10.1090/proc/14250

APA

Barthel, T., & Bousfield, A. K. (2019). On the comparison of stable and unstable P-completion. Proceedings of the American Mathematical Society, 147(2), 897-908. https://doi.org/10.1090/proc/14250

Vancouver

Barthel T, Bousfield AK. On the comparison of stable and unstable P-completion. Proceedings of the American Mathematical Society. 2019;147(2):897-908. https://doi.org/10.1090/proc/14250

Author

Barthel, Tobias ; Bousfield, A. K. / On the comparison of stable and unstable P-completion. I: Proceedings of the American Mathematical Society. 2019 ; Bind 147, Nr. 2. s. 897-908.

Bibtex

@article{1b7bf9fc84bb46d3b677828d42943dde,
title = "On the comparison of stable and unstable P-completion",
abstract = "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.",
author = "Tobias Barthel and Bousfield, {A. K.}",
year = "2019",
doi = "10.1090/proc/14250",
language = "English",
volume = "147",
pages = "897--908",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "2",

}

RIS

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