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Maps between p-completed classifying spaces

Published online by Cambridge University Press:  14 November 2011

J. Frank Adams  and
Zdzisław Wojtkowiak
J. Frank Adams
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1SB, U.K
Zdzisław Wojtkowiak
Affiliation:
Universitat Autònoma de Barcelona, Departament de Matemàtiques, 08193 Bellaterra, Barcelona, Spain
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Synopsis

Let G and G' be two connected compact Lie groups with maximal tori T and T'. For a space X, let Xp be the p-completion of X. We will associate to each topological map f:(BG)p→(BG')p an “admissible map” ϕ:π1(T)⊗zZp→π1(T′)⊗zZp. We then show that the study of “admissible maps” in the p-complete case may be reduced to their study in the p-local case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 112 , Issue 3-4 , 1989 , pp. 231 - 235
Copyright
Copyright © Royal Society of Edinburgh 1989

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References

1Adams, J. F. and Mahmud, Z.. Maps between classifying spaces. Invent. Math. 35 (1976), 1–41.CrossRefGoogle Scholar
2Dwyer, W. and Zabrodsky, A.. Maps between classifying spaces. In Algebraic Topology, Barcelona 1986, Lecture Notes in Mathematics 1298 pp. 106–119 (Berlin: Springer-Verlag 1987).CrossRefGoogle Scholar