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Localized stable homotopy of some classifying spaces

Published online by Cambridge University Press:  24 October 2008

Victor Snaith
Victor Snaith
Affiliation:
The University of Western Ontario, London, Ontario, Canada
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Extract

In this note I will give new, simplified proofs of some of the results announced in (18) and proved in ((19), I, § 4, II, §§ 2, 9).These results mostly date from 1975/6 at which time they were proved using my crude stable decomposition of ωn σnX (20) and differential-geometric techniques with the Becker-Gottlieb transfer. Since then more systematic approaches have been developed towards the stable decompositions ((4); (5); (6); (10); (12)) and towards the transfer ((7), I and II; (8)). Actually, the system-atization of the stable decompositions was already latent in (15) if only I had realized it!

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 2 , March 1981 , pp. 325 - 330
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

(1)Atiyah, M. F.K-theory (Benjamin, 1968).Google Scholar
(2)Becker, J. C. and Gottlieb, D. H.The transfer map and fibre bundles; Topology 14 (1975), 1–12.CrossRefGoogle Scholar
(3)Becker, J. C. and Gottlieb, D. H.Transfer maps for fibrations and duality; Compositio Math. (To appear.)Google Scholar
(4)Caruso, J., Cohen, F. R., May, J. P. and Taylor, L. R. James maps, Segal maps and the Kahn–Priddy theorem. (To appear.)Google Scholar
(5)Cohen, F. R., May, J. P. and Taylor, L. R.Splitting of certain spaces CX. Math. Proc. Cambridge Philos. Soc. 84 (1978), 465–496.CrossRefGoogle Scholar
(6)Cohen, F. R., May, J. P. and Taylor, L. R.Splitting of more spaces. Math. Proc. Cambridge Philos. Soc. 86 (1979), 227–236.CrossRefGoogle Scholar
(7)Feshbach, M. The transfer and compact Lie groups. 1: Thesis Stanford (1976), II: Trans. Amer. Math. Soc. 251 (1979), 139–169.Google Scholar
(8)Feshbach, M.The transfer and compact Lie groups. Bull. Amer. Math. Soc. 83 (1977), 372–374.CrossRefGoogle Scholar
(9)Harris, B. and Segal, G. B.K1 groups of algebraic integers. Annals of Math. 101 (1975), 20–33.CrossRefGoogle Scholar
(10)Koschorke, U. and Sanderson, B.Self-intersections and higher Hopf invariants. Topology 17 (1978), 282–290.CrossRefGoogle Scholar
(11)Mahowald, M.A new infinite family in . Topology 16 (1977), 249–256.CrossRefGoogle Scholar
(12)May, J. P. Applications and generalisations of the approximation theorem. Conference Proceedings Aarhus (1978).CrossRefGoogle Scholar
(13)May, J. P.Geometry of iterated loopspaces. Lecture Notes in Mathematics, no. 271, Springer-Verlag (1972).CrossRefGoogle Scholar
(14)Mosher, R. E.Some stable homotopy of complex projective space. Topology 7 (1968), 179–193.CrossRefGoogle Scholar
(15)Segal, G. B.Operations in stable homotopy. London Math. Soc. Lecture Notes, no. 11 (1974), 105–110.Google Scholar
(16)Segal, G. B.The stable homotopy of complex projective space. Quart. J. Math. (Oxford) 24 (1973), 1–5.CrossRefGoogle Scholar
(17)Snaith, V. P.Stable decomposition of ωnSnX. J. London Math. Soc. (2) 7 (1974), 577–583.CrossRefGoogle Scholar
(18)Snaith, V. P.Towards algebraic cobordism. Bull. Amer. Math. Soc. 83, no. 3 (1977).CrossRefGoogle Scholar
(19)Snaith, V. P.Algebraic cobordism and K-theory. Mem. Amer. Math. Soc. no. 221 (1979).CrossRefGoogle Scholar
(20) Problem session. Amer. Soc. Summer Institute, Stanford (1976).Google Scholar
(21)Toda, H.Mem. Coll. Sci. Univ. Kyoto 32 (1959), 103–119.Google Scholar