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

DOI:
https://doi.org/10.1090/S0002-9939-97-03744-1

MathSciNet review:
1371135

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Abstract | References | Similar Articles | Additional Information

Abstract: There is a localization functor with the property that is the -completion of whenever is a finite dimensional complex. This same functor is shown to have the property that is contractible whenever is a connected infinite loop space with a torsion fundamental group. One consequence of this is that many finite dimensional complexes are uniquely determined, up to -completion, by the homotopy fiber of any map from into the classifying space .

**1.**J. F. Adams,*The Kahn-Priddy theorem*, Proc. Camb. Phil. Soc. (1973)**73**45-55. MR**46:9976****2.**A. K. Bousfield and D. M. Kan,*Homotopy Limits, Completions and Localizations*, Lecture Notes in Math.**304**, Springer, 1972. MR**51:1825****3.**C. Casacuberta,*Recent advances in unstable localization*, CRM Lecture Notes**6**, (1994), 1-22. MR**95e:55014****4.**E. Dror Farjoun,*Homotopy localization and -periodic spaces*Springer Lecture Notes in Math.**1509**, (1991), 104-113. MR**93k:55013****5.**E. Dror Farjoun,*Localizations, fibrations and conic structures*, preprint 1992.**6.**E. Dror Farjoun,*Cellular spaces*, preprint 1993.**7.**E. Dror Farjoun,*Cellular inequalities*, Contemporary Math.**181**(1995), 159-181. CMP**95:09****8.**C. A. McGibbon,*A note on Miller's theorem about maps out of certain classifying spaces*, Proc. Amer. Math. Soc., to appear.**9.**H. Miller,*The Sullivan fixed point conjecture on maps from classifying spaces*, Annals of Math.**120**(1984) 39-87;**121**(1985), 605-609. MR**85i:55012**; MR**87k:55020****10.**J. A. Neisendorfer,*Localization and connected covers of finite complexes*, Contemporary Math.**181**(1995), 385-390. MR**96a:55019**

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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:
https://doi.org/10.1090/S0002-9939-97-03744-1

Received by editor(s):
August 10, 1995

Communicated by:
Thomas Goodwillie

Article copyright:
© Copyright 1997
American Mathematical Society