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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Infinite loop spaces
and Neisendorfer localization


Author: C. A. McGibbon
Journal: Proc. Amer. Math. Soc. 125 (1997), 309-313
MSC (1991): Primary 55P47, 55P60, 55P65
MathSciNet review: 1371135
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Abstract: There is a localization functor $L$ with the property that $L(X)$ is the $p$-completion of $X$ whenever $X$ is a finite dimensional complex. This same functor is shown to have the property that $L(E)$ is contractible whenever $E$ is a connected infinite loop space with a torsion fundamental group. One consequence of this is that many finite dimensional complexes $X$ are uniquely determined, up to $p$-completion, by the homotopy fiber of any map from $X$ into the classifying space $B \! E$.


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Additional Information

C. A. McGibbon
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email: mcgibbon@math.wayne.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03744-1
PII: S 0002-9939(97)03744-1
Received by editor(s): August 10, 1995
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1997 American Mathematical Society