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The uniqueness of bundle transfers

Published online by Cambridge University Press:  24 October 2008

L. G. Lewis Jr
L. G. Lewis Jr
Affiliation:
Syracuse University
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Abstract

Let K be a cohomology theory. Axioms are given which uniquely characterize the transfer in K-cohomology for bundles with structure group a compact Lie group and fibre a finite C.W. complex. Also, a family of generalized transfers is defined which includes both the standard transfer and Atiyah's holomorphic transfer.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 1 , January 1983 , pp. 87 - 111
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

(1)Adams, J. F. Infinite loop spaces. Annals of Mathematics Studies, vol. 90 (Princetown Univ. Press, 1978).Google Scholar
(2)Atiyah, M. F.Bott periodicity and the index of elliptic operators. Quart. J. Math. Oxford 19 (1968), 113–140.CrossRefGoogle Scholar
(3)Atiyah, M. F.K-theory (W. A. Benjamin, New York, 1967).Google Scholar
(4)Atiyah, M. F. and Segal, G. B.Equivariant K-theory and completion. J. Diff. Geom. 3 (1969), 1–18.Google Scholar
(5)Becker, J. C. On the transfer for finite covering spaces. (Preprint.)Google Scholar
(6)Becker, J. C. and Gottlieb, D. H.The transfer for fiber bundles, Topology 14 (1975), 1–12.CrossRefGoogle Scholar
(7)Becker, J. C. and Gottlieb, D. H.Transfer maps for fibrations and duality. Compositio Math. 33 (1976), 107–133.Google Scholar
(8)Clapp, M.Duality and transfer for parametrized spectra. Arch. Math. 37 (1981), 462–472.CrossRefGoogle Scholar
(9)Dold, A.The fixed point transfer of fibre preserving maps. Math. Zeit. 148 (1976), 215–244.CrossRefGoogle Scholar
(10)Dold, A. and Puppe, D. Duality, trace, and transfer. Proc. of the International Conference on Geometric Topology (Polish Scientific Publishers, Warsaw, 1980), 81–102.Google Scholar
(11)Feshbach, M.The transfer and compact Lie groups. Trans. Amer. Math. Soc. 251 (1979), 139–169.CrossRefGoogle Scholar
(12)Illman, S.Smooth equivariant triangulations of G-manifolds for G a finite group. Math. Ann. 233 (1978), 199–220.CrossRefGoogle Scholar
(13)Lashof, R. K.Equivariant bundles. Illinois J. Math. 26 (1982), 257–271.CrossRefGoogle Scholar
(14)Lewis, L. G., May, J. P., McClure, J. E. and Steinberger, M.Equivariant stable homotopy theory. Springer Lecture Notes in Mathematics (in preparation).Google Scholar
(15)Matumoto, T.Equivariant K-theory and Fredholm operators. J. Fac. Sci. Univ. Tokyo, series 1A 18 (1971), 109–125.Google Scholar
(16)May, J. P.Classifying spaces and fibrations. Amer. Math. Soc. Memo. 155 (1975).Google Scholar
(17)May, J. P. E∞ ring spaces and E∞ ring spectra. Springer Lecture Notes in Mathematics, no. 577 (Springer, New York, 1970).Google Scholar
(18)May, J. P. and McClure, J. E.A reduction of the Segal conjecture. Current Trends in Algebraic Topology. Canadian Mathematical Society Conference Proceedings, vol. 2 (to appear).Google Scholar
(19)Nishida, G.The transfer homomorphism in equivariant generalized cohomology theories. J. Math. Kyoto 18 (1978), 435–451.CrossRefGoogle Scholar
(20)Roush, F. W. Transfer in generalized cohomology theories. Thesis, Princeton University, 1971.Google Scholar
(21)Verona, A.Triangulation of stratified fibre bundles. Manu. Math. 30 (1979/1980), 425–445.CrossRefGoogle Scholar
(22)Waner, S.Equivariant classifying spaces and fibrations. Trans. Amer. Math. Soc. 258 (1980), 385–406.CrossRefGoogle Scholar
(23)Waner, S.Equivariant fibrations and transfer. Trans. Amer. Math. Soc. 258 (1980), 369–384.CrossRefGoogle Scholar
(24)Wirthmüller, K.Equivariant S-duality. Arch. Math. 26 (1975), 427–431.CrossRefGoogle Scholar