Infinite loop spaces and Neisendorfer localization
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- by C. A. McGibbon PDF
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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 $B E$.References
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Additional Information
- C. A. McGibbon
- Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
- Email: mcgibbon@math.wayne.edu
- Received by editor(s): August 10, 1995
- Communicated by: Thomas Goodwillie
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 309-313
- MSC (1991): Primary 55P47, 55P60, 55P65
- DOI: https://doi.org/10.1090/S0002-9939-97-03744-1
- MathSciNet review: 1371135