Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on Miller's theorem about maps
out of classifying spaces


Author: C. A. McGibbon
Journal: Proc. Amer. Math. Soc. 124 (1996), 3241-3245
MSC (1991): Primary 55R35, 55P47, 55S37
DOI: https://doi.org/10.1090/S0002-9939-96-03407-7
MathSciNet review: 1328362
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $X$ be a connected infinite loop space whose fundamental group is a torsion group and let $Y$ be a finite nilpotent $CW$-complex. The main result of this paper is that the space of based maps from $X$ to the profinite completion of $Y$ is weakly contractible.


References [Enhancements On Off] (What's this?)

  • 1. A. K. Bousfield and D. M. Kan, Homotopy Limits, Completions and Localizations, Lecture Notes in Math. 304, Springer, 1972. MR 51:1825
  • 2. F. R. Cohen, T. J. Lada, and J. P. May, The homology of iterated loop spaces, Lecture Notes in Math. 533, Springer, 1976. MR 55:9096
  • 3. E. Friedlander and G. Mislin, Locally finite approximations of Lie groups, Inventiones Math. 83 (1986) 425--436. MR 87i:55038
  • 4. B. Gray and C. A. McGibbon, Universal phantom maps, Topology 32 (1993) 371--394. MR 94a:55008
  • 5. C. A. McGibbon, Phantom maps, a chapter in The Handbook of Algebraic Topology, I. M. James, ed., North Holland, 1995.
  • 6. H. Miller, The Sullivan conjecture on maps from classifying spaces, Annals of Math. 120 (1984) 39--87. MR 85i:55012
  • 7. S. B. Priddy, On $\Omega ^{\infty }S^{\infty }$ and the infinite symmetric group, Proc. Symp. Pure Math. AMS 22 (1971) 217--220. MR 50:11226
  • 8. D. Sullivan, Genetics of homotopy theory and the Adams conjecture, Annals of Math. 100 (1974) 1--79. MR 56:1305
  • 9. A. Zabrodsky, On phantom maps and a theorem of H. Miller, Israel J. Math. 58 (1987) 129--143. MR 88m:55028

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 55R35, 55P47, 55S37

Retrieve articles in all journals with MSC (1991): 55R35, 55P47, 55S37


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/S0002-9939-96-03407-7
Received by editor(s): January 10, 1995
Received by editor(s) in revised form: April 4, 1995
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society