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Uniqueness of BSO

Published online by Cambridge University Press:  24 October 2008

J. F. Adams  and
S. B. Priddy
J. F. Adams
Affiliation:
University of Cambridge and Northwestern University
S. B. Priddy
Affiliation:
University of Cambridge and Northwestern University
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Extract

This paper will show that after localization at any given prime p, the infinite loop space structure on the space BSO is essentially unique. If the word ‘localization’ is replaced by ‘completion’, the result continues to hold; and both results continue to hold if the space BSO is replaced by the space BSU.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 3 , November 1976 , pp. 475 - 509
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

REFERENCES

(1)Adams, J. F.On Chern characters and the structure of the unitary group. Proc. Camb. Philos. Soc. 57 (1961), 189–199.CrossRefGoogle Scholar
(2)Adams, J. F.Stable homotopy and generalized homology (Chicago University Press, 1974).Google Scholar
(3)Adams, J. F. and Margolis, H. R.Modules over the Steenrod algebra. Topology 10 (1971), 271–282.CrossRefGoogle Scholar
(4)Atiyah, M. F. and Segal, G. B.Exponential isomorphisms for λ-rings. Quart. J. Math. 22 (1971), 371–378.CrossRefGoogle Scholar
(5)Boardman, J. M. and Vogt, R. M.Homotopy-everything H-spaces. Bull. Amer. Math. Soc. 74 (1968), 1117–1122.CrossRefGoogle Scholar
(6)Madsen, I., Snaith, V. and Tornehave, J.H ∞ endomorphisme of K-theory are infinite loop maps. (Manuscript.)Google Scholar
(7)May, J. P.E ∞. spaces, group completions, and permutative categories. London Math. Soc. Lecture Note, series no. 11 (Cambridge University Press, 1974).CrossRefGoogle Scholar
(8)May, J. P.E ∞ ring spaces and E ∞ ring spectra. (To appear.)Google Scholar
(9)May, J. P.Localisations, completions, and the stabilisation of homotopy theory (London Math. Soc. Monograph). (To appear.)Google Scholar
(10)Priddy, S. B.Homology operations for the classifying spaces of certain matrix groups. Quart. J. Math. 26 (1975) 179–193.CrossRefGoogle Scholar
(11)Peterson, F. P.The mod p homotopy type of BSO and F/PL. Bol. Soc. Mat. Mexican 14 (1969), 22–27.Google Scholar
(12)Segal, G. B.Categories and cohomology theories. Topology 13 (1974), 293–312.CrossRefGoogle Scholar
(13)Sullivan, D.Genetics of homotopy theory and Adams conjecture. Ann. of Math. 100 (1974), 1–79.CrossRefGoogle Scholar
(14)Sullivan, D. Geometric topology. Part I. Localization, periodicity and Galois symmetry (mimeographed notes, M.I.T. 1970).Google Scholar