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The Kahn–Priddy theorem

Published online by Cambridge University Press:  24 October 2008

J. F. Adams
J. F. Adams
Affiliation:
D.P.M.M.S., Cambridge
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Extract

Let ΦSr(X) be the stable homotopy group

where SnX means the n-fold suspension of X. For example, the groups ΦSr(S0) are the stable homotopy groups of spheres. Let

be the ‘infinite-dimensional’ orthogonal group. Then topologists are familiar with the ‘stable J-homomorphism’

G. W. Whitehead observed that J factors through an ‘even more stable’ J-homomorphism

he conjectured that J′ is epi (for r > 0).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 1 , January 1973 , pp. 45 - 55
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Adams, J. F.Stable Homotopy, lecture notes, University of Chicago 1972.Google Scholar
(2)Brown, E. H.Cohomology theories. Ann. of Math. (2) 75 (1962), 467–484.Google Scholar
(3)James, I. M.On the suspension sequence. Ann. of Math. (2) 65 (1957), 74–107.Google Scholar
(4)Kahn, D. S. and Priddy, S. B.Applications of the transfer to stable homotopy theory (preprint).CrossRefGoogle Scholar
(5)Steenrod, N. E.Cyclic reduced powers of cohomology classes. Proc. Nat. A. Sci. USA 39 (1953), pp. 217–223, especially Theorem 4.8, pp. 218–219.Google Scholar
(6)Vogt, R.Boardman's Stable Homotopy Category, Aarhus University (Lecture Notes series No. 21), 1970.Google Scholar