Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T07:31:02.731Z Has data issue: false hasContentIssue false

The 2-primary J-homomorphism

Published online by Cambridge University Press:  24 October 2008

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

Extract

In this paper every space will be 2-local, for example BO will mean the 2-localization of the space usually denoted BO.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Adams, J. F.On the groups J(X). I and IV. Topology 2 (1963), 181195; Topology 5 (1966), 21–80.CrossRefGoogle Scholar
(2)Becker, J. C.Characteristic classes and K-theory; Lecture Notes in Mathematics, no. 428 (1975), 132143.Google Scholar
(3)Becker, J. C. and Gottlieb, D. H.The transfer map and fibre bundles. Topology 14 (1975), 112.CrossRefGoogle Scholar
(4)Becker, J. C. and Gottlieb, D. H.Transfer maps for fibrations and duality. Compositio Math. (in the Press).Google Scholar
(5)Brumfiel, G. and Madsen, I.Evaluation of the transfer and the universal surgery classes. Inventiones Math. 32 (1976), 133169.CrossRefGoogle Scholar
(6)Clough, R. R.The map SJSF does not deloop mod 2. Canad. J. Math. 17 (1975), 737745.CrossRefGoogle Scholar
(7)Clough, R. R. and Stasheff, J. D.BSJ does not map correctly into BSF mod 2. Manu-scripta Math. 7 (1972), 205214.CrossRefGoogle Scholar
(8)Husemoller, D.Fibre bundles (McGraw-Hill, 1966).CrossRefGoogle Scholar
(9)James, I. M.Bundles with special structure: I. Ann. of Math. 89 (1969), 359390.CrossRefGoogle Scholar
(10)Madsen, I. Private communication.Google Scholar
(11)Madsen, I.Higher torsion in SG and BSG. Math. Z. 143 (1975), 5580.CrossRefGoogle Scholar
(12)Madsen, I.On the action of the Dyer-Lashof algebra on H*, (G). Pacific J. Math. 60 (1975), 235275.CrossRefGoogle Scholar
(13)Madsen, I., Snaith, V. and Tornehave, J.Infinite loop maps in geometric topology. (Aarhus Universitet Preprint Series 31 (1974/5)) Math. Proc. Cambridge Philos Soc. 81 (1977), 399430.CrossRefGoogle Scholar
(14)May, J. P. (with contributions by F. Quinn and N. Ray): E ring spaces and E ring spectra (to appear).Google Scholar
(15)May, J. P.The geometry of iterated loop spaces. Lecture Notes in Mathematics, no. 271 (1972).CrossRefGoogle Scholar
(16)Quillen, D. G.The Adams conjecture. Topology 10 (1971), 6780.CrossRefGoogle Scholar
(17)Seymour, R. M.Vector bundles invariant under the Adams operations. Quart. J. Math. Oxford Ser. (2) 25 (1975), 395414.CrossRefGoogle Scholar
(18)Seymour, R. M.The infinite loop Adams conjecture. University College preprint (1976).Google Scholar
(19)Snaith, V. P.Dyer-Lashof operations in K-theory, Lecture Notes in Mathematics, no. 496 (1976), 104294.Google Scholar
(20)Snaith, V. P.The complex J-homomorphism. I. Proc. London Math. Soc. 34 (1977), 269302.CrossRefGoogle Scholar
(21)Snaith, V. P.Algebraic cobordism and K-theory. (Submitted to Mem. Amer. Math. Soc.)Google Scholar
(22)Sullivan, D.Genetics of homotopy theory and the Adams conjecture. Ann. of Math. 100 (1974), 179.CrossRefGoogle Scholar
(23)Toda, H.Composition methods in homotopy groups of spheres. Ann. of Math., study no. 49 (1962).Google Scholar
(24)Tornehave, J. Deviation from additivity of a solution of the Adams conjecture (lecture given at Am. Math. Soc. Summer Inst., Stanford, 1976).Google Scholar