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The transfer and stable homotopy theory

Published online by Cambridge University Press:  24 October 2008

Daniel S. Kahn  and
Stewart B. Priddy
Daniel S. Kahn
Affiliation:
Northwestern University, Evanston, Illinois, U.S.A.
Stewart B. Priddy
Affiliation:
Northwestern University, Evanston, Illinois, U.S.A.
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Extract

The purpose of this paper is to give a proof of the following splitting theorem in stable homotopy theory. We assume all spaces are localized at a fixed prime p. Let k be the symmetric group on {1, …, k}, Q(.) = lim ΩnΣn(.), and QkS0, k ∈ , denote the components of QS0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 1 , January 1978 , pp. 103 - 111
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1) Adams, J. F. The Kahn-Priddy theorem. Proc. Cambridge Philos. Soc. 73 (1973), 45–55.CrossRefGoogle Scholar
(2) Becker, J. and Gottlieb, D. The transfer map and fibre bundles. Topology 14 (1975), 1–12.CrossRefGoogle Scholar
(3) Becker, J. and Schultz, R. Equivariant function spaces and stable homotopy theory.(To appear.)Google Scholar
(4) Barratt, M. G., Kahn, D. S. and Priddy, S. B. On Ω∞ S∞ and the infinite symmetric group. Proc. Symp. Pure Math. 22 (A.M.S. 1971).Google Scholar
(5) Boardman, J. and Vogt, R. Homotopy-everything H-spaces. Bull.Amer. Math. Soc. 74 (1968), 1117–1122.CrossRefGoogle Scholar
(6) Bredon, G. E. Equivariant cohomology theory. Lecture Notes in Mathematics no. 34.Google Scholar
(7) Dold, A. Transfert des points fixés d'une famille continue d'applications. C. R. Acad. Sci. Paris 278 (1974), 1291–1293.Google Scholar
(8) Dyer, E. and Lashof, R. Homology of iterated loop spaces. Amer. J. Math. 84 (1962), 35–88.CrossRefGoogle Scholar
(9) Evens, L. A generalization of the transfer map in the cohomology of groups. Trans. Amer. Math. Soc. 108 (1963), 54–65.CrossRefGoogle Scholar
(10) Kahn, D. S. Homology of the Barratt-Eccles decomposition maps. Notes de Mathematics y Symposia, no. 1 (Soc. Mat. Mexioana, 1975).Google Scholar
(11) Kahn, D. S. and Priddy, S. B. Applications of the transfer to stable homotopy theory. Bull. Amer. Math. Soc. 78 (1972), 981–987.CrossRefGoogle Scholar
(12) Kahn, D. S. and Priddy, S. B. Transfer, symmetric groups and stable homotopy theory: algebraic K-theory 1. Lecture Notes in Mathematics, no. 341.Google Scholar
(13) Kahn, D. S. and Priddy, S. B. On the transfer in the homology of symmetric groups. Math. Proc. Cambridge Philos. Soc. 83 (1978), 91–101.CrossRefGoogle Scholar
(14) May, J. P. The geometry of iterated loop spaces. Lecture Notes in Mathematics, no. 271.Google Scholar
(15) May, J. P. Categories of spectra and infinite loop spaces, category theory, homology theory and their applications. Lecture Notes in Mathematics, no. 99.Google Scholar
(16) Nakaoka, M. Homology of the infinite symmetric group. Ann. of Math. (2) 73 (1961), 229–257.CrossRefGoogle Scholar
(17) Nishida, G. The nilpotency of elements of the stable homotopy groups of spheres. J. Math. Soc. Japan 25 (1973), 707–732.CrossRefGoogle Scholar
(18) Priddy, S. B. Homotopy splittings involving G and G/O. (To appear.)Google Scholar
(19) Ray, N. A geometrical observation on the Arf invariant of a framed manifold. Bull. London Math. Soc. 4 (1972), 163–164.CrossRefGoogle Scholar
(20) Roush, F. W. Transfer in generalized cohomology theories. Princeton Thesis (1971).Google Scholar
(21) Segal, G. Operations in stable homotopy theory. In New developmentsin topology, pp. 105–110 (Cambridge University Press, 1974).CrossRefGoogle Scholar
(22) Whitehead, J. H. C. Combinatorial homotopy: I. Bull. Amer. Math. Soc. 55 (1949), 213–245.CrossRefGoogle Scholar