Skip to main content Accesibility Help

Localized stable homotopy of some classifying spaces

  • Victor Snaith (a1)

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!

Hide All
(1)Atiyah, M. F.K-theory (Benjamin, 1968).
(2)Becker, J. C. and Gottlieb, D. H.The transfer map and fibre bundles; Topology 14 (1975), 112.
(3)Becker, J. C. and Gottlieb, D. H.Transfer maps for fibrations and duality; Compositio Math. (To appear.)
(4)Caruso, J., Cohen, F. R., May, J. P. and Taylor, L. R. James maps, Segal maps and the Kahn–Priddy theorem. (To appear.)
(5)Cohen, F. R., May, J. P. and Taylor, L. R.Splitting of certain spaces CX. Math. Proc. Cambridge Philos. Soc. 84 (1978), 465496.
(6)Cohen, F. R., May, J. P. and Taylor, L. R.Splitting of more spaces. Math. Proc. Cambridge Philos. Soc. 86 (1979), 227236.
(7)Feshbach, M. The transfer and compact Lie groups. 1: Thesis Stanford (1976), II: Trans. Amer. Math. Soc. 251 (1979), 139169.
(8)Feshbach, M.The transfer and compact Lie groups. Bull. Amer. Math. Soc. 83 (1977), 372374.
(9)Harris, B. and Segal, G. B.K1 groups of algebraic integers. Annals of Math. 101 (1975), 2033.
(10)Koschorke, U. and Sanderson, B.Self-intersections and higher Hopf invariants. Topology 17 (1978), 282290.
(11)Mahowald, M.A new infinite family in . Topology 16 (1977), 249256.
(12)May, J. P. Applications and generalisations of the approximation theorem. Conference Proceedings Aarhus (1978).
(13)May, J. P.Geometry of iterated loopspaces. Lecture Notes in Mathematics, no. 271, Springer-Verlag (1972).
(14)Mosher, R. E.Some stable homotopy of complex projective space. Topology 7 (1968), 179193.
(15)Segal, G. B.Operations in stable homotopy. London Math. Soc. Lecture Notes, no. 11 (1974), 105110.
(16)Segal, G. B.The stable homotopy of complex projective space. Quart. J. Math. (Oxford) 24 (1973), 15.
(17)Snaith, V. P.Stable decomposition of ωnSnX. J. London Math. Soc. (2) 7 (1974), 577583.
(18)Snaith, V. P.Towards algebraic cobordism. Bull. Amer. Math. Soc. 83, no. 3 (1977).
(19)Snaith, V. P.Algebraic cobordism and K-theory. Mem. Amer. Math. Soc. no. 221 (1979).
(20) Problem session. Amer. Soc. Summer Institute, Stanford (1976).
(21)Toda, H.Mem. Coll. Sci. Univ. Kyoto 32 (1959), 103119.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed