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A Kahn-Priddy sequence and a conjecture of G. W. Whitehead

Published online by Cambridge University Press:  24 October 2008

Nicholas J. Kuhn
Nicholas J. Kuhn
Affiliation:
Princeton University
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Extract

In this paper we simultaneously prove a conjecture of G. W. Whitehead concerning symmetric product spectra and extend the epimorphism of the Kahn-Priddy Theorem to a long exact sequence. This sequence can be interpreted as a minimal resolution of the integral Eilenberg-MacLane spectrum by suspension spectra.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 3 , November 1982 , pp. 467 - 483
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

(1)Adem, J. The relations on Steenrod powers of cohomology classes. In Algebraic-geometry and topology, ed. Fox, R. H. et al. (Princeton University Press, 1957), pp. 191–242.CrossRefGoogle Scholar
(2)Cohen, F. R., Lada, T. J. and May, J. P.The homology of iterated loop spaces. Springer Lecture Notes in Mathematics, no. 533, 1976.CrossRefGoogle Scholar
(3)Dold, A. and Thom, R.Quasifaserungen und unendliche symmetrische Produkte. Ann. of Math. 67 (1958), 239–281.CrossRefGoogle Scholar
(4)Finkelstein, L. Thesis, Northwestern University (1978).Google Scholar
(5)James, I. M., Thomas, E., Toda, H. and Whitehead, G. W.On the symmetric square of a sphere. J. of Math. and Mech. 12 (1963), 771–776.Google Scholar
(6)Kahn, D. S.On the stable decomposition of Ω∞S ∞A. Springer Lecture Notes in Mathematics, no. 658 (1978), 206–213.CrossRefGoogle Scholar
(7)Kahn, D. S. and Priddy, S. B.Applications of the transfer to stable homotopy theory. Bull. Amer. Math. Soc. 76 (1972), 981–987.CrossRefGoogle Scholar
(8)Kuhn, N. J.The homology of the James-Hopf maps. Illinois J. Math. (To appear.)Google Scholar
(9)Milgram, R. J. (ed.). Problems presented to the 1970 AMS Summer Colloquium in Algebraic Topology. In Algebraic Topology, Proc. Symp. Pure Math. XXII. AMS (1971), pp. 187–201.Google Scholar
(10)Miller, H. R.A spectral sequence for the homology of an infinite delooping. Pac. J. Math. 79 (1978), 139–155.CrossRefGoogle Scholar
(11)Miller, H. R. An algebraic analogue of a conjecture of G. W. Whitehead. (To appear.)Google Scholar
(12)Mitchell, S. Thesis, University of Washington (1981).Google Scholar
(13)Mitchell, S. and Priddy, S. B. (In preparation.)Google Scholar
(14)Nakaoka, M.Cohomology mod p of symmetric products of spheres. J. Inst. Poly. (Osaka City Univ.), 9 (1958), 1–18.Google Scholar
(15)Tsuchiya, A.Homology operations on ring spectra of H ∞ type and their applications. J. Math. Soc. Japan 25 (1973), 277–316.CrossRefGoogle Scholar
(16)Welcher, P. J.Symmetric products and the stable Hurewicz homomorphism. Illinois J. Math. 24, no. 4 (1980), 527–544.CrossRefGoogle Scholar