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 | 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. Cambridge Philos. Soc.**73**(1973), 45–55. MR**0310878****2.**A. K. Bousfield and D. M. Kan,*Homotopy limits, completions and localizations*, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR**0365573****3.**Carles Casacuberta,*Recent advances in unstable localization*, The Hilton Symposium 1993 (Montreal, PQ), CRM Proc. Lecture Notes, vol. 6, Amer. Math. Soc., Providence, RI, 1994, pp. 1–22. MR**1290581****4.**Emmanuel Dror Farjoun,*Homotopy localization and 𝑣₁-periodic spaces*, Algebraic topology (San Feliu de Guíxols, 1990) Lecture Notes in Math., vol. 1509, Springer, Berlin, 1992, pp. 104–113. MR**1185964**, 10.1007/BFb0087504**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.**Haynes Miller,*The Sullivan conjecture on maps from classifying spaces*, Ann. of Math. (2)**120**(1984), no. 1, 39–87. MR**750716**, 10.2307/2007071

Haynes Miller,*Correction to: “The Sullivan conjecture on maps from classifying spaces” [Ann. of Math. (2) 120 (1984), no. 1, 39–87; MR0750716 (85i:55012)]*, Ann. of Math. (2)**121**(1985), no. 3, 605–609. MR**794376**, 10.2307/1971212**10.**Joseph A. Neisendorfer,*Localization and connected covers of finite complexes*, The Čech centennial (Boston, MA, 1993) Contemp. Math., vol. 181, Amer. Math. Soc., Providence, RI, 1995, pp. 385–390. MR**1321002**, 10.1090/conm/181/02044

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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