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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!

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(2) J. C. Becker and D. H. Gottlieb The transfer map and fibre bundles; Topology 14 (1975), 112.

(8) M. Feshbach The transfer and compact Lie groups. Bull. Amer. Math. Soc. 83 (1977), 372374.

(9) B. Harris and G. B. Segal K1 groups of algebraic integers. Annals of Math. 101 (1975), 2033.

(10) U. Koschorke and B. Sanderson Self-intersections and higher Hopf invariants. Topology 17 (1978), 282290.

(11) M. Mahowald A new infinite family in . Topology 16 (1977), 249256.

(13) J. P. May Geometry of iterated loopspaces. Lecture Notes in Mathematics, no. 271, Springer-Verlag (1972).

(14) R. E. Mosher Some stable homotopy of complex projective space. Topology 7 (1968), 179193.

(16) G. B. Segal The stable homotopy of complex projective space. Quart. J. Math. (Oxford) 24 (1973), 15.

(18) V. P. Snaith Towards algebraic cobordism. Bull. Amer. Math. Soc. 83, no. 3 (1977).

(19) V. P. Snaith Algebraic cobordism and K-theory. Mem. Amer. Math. Soc. no. 221 (1979).

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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