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Quillen's work on the Adams Conjecture

Published online by Cambridge University Press:  11 March 2013

W. G. Dwyer
W. G. Dwyer*
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, USAdwyer.1@nd.edu
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Abstract

In the 1960's and 1970's, the Adams Conjecture figured prominently both in homotopy theory and in geometric topology. Quillen sketched one way to attack the conjecture and then proved it with an entirely different line of argument. Both of his approaches led to spectacular and beautiful new mathematics.

Keywords

Adams Conjecturealgebraic K-theorygroup cohomologyPrimary 55N15Secondary 18F2520J06
Type
Research Article
Information
Journal of K-Theory , Volume 11 , Issue 3: The Legacy of Daniel Quillen , June 2013 , pp. 517 - 526
Copyright
Copyright © ISOPP 2013 

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References

REFERENCES

1.Adams, J. F., Vector fields on spheres, Ann. of Math. (2) 75 (1962), 603–632.CrossRefGoogle Scholar
2.Adams, J. F., On the groups J(X). I, Topology 2 (1963), 181–195.Google Scholar
3.Adams, J. F., On the groups J(X). II, Topology 3 (1965), 137–171.Google Scholar
4.Adams, J. F., On the groups J(X). III, Topology 3 (1965), 193–222.Google Scholar
5.Adams, J. F., Infinite loop spaces, Annals of Mathematics Studies 90, Princeton University Press, Princeton, N.J., 1978.Google Scholar
6.Artin, M. and Mazur, B., Etale homotopy, Lecture Notes in Mathematics 100, Springer-Verlag, Berlin, 1969.Google Scholar
7.Atiyah, M. F., Thom complexes, Proc. London Math. Soc. (3) 11 (1961), 291–310.Google Scholar
8.Becker, J. C. and Gottlieb, D. H., The transfer map and fiber bundles, Topology 14 (1975), 1–12.Google Scholar
9.Friedlander, E. M., Fibrations in etale homotopy theory, Inst. Hautes Études Sci. Publ. Math. 42 (1973), 5–46.Google Scholar
10.Friedlander, E. M., Étale homotopy of simplicial schemes, Annals of Mathematics Studies 104, Princeton University Press, Princeton, N.J., 1982.Google Scholar
11.Madsen, I. and Milgram, R. J., The classifying spaces for surgery and cobordism of manifolds, Annals of Mathematics Studies 92, Princeton University Press, Princeton, N.J., 1979.Google Scholar
12.May, J. P., Infinite loop space theory, Bull. Amer. Math. Soc. 83(4) (1977), 456–494.Google Scholar
13.Milnor, J. W. and Kervaire, M. A., Bernoulli numbers, homotopy groups, and a theorem of Rohlin, Proc. Internat. Congress Math. 1958, Cambridge Univ. Press, New York, 1960, 454–458.Google Scholar
14.Quillen, D. G., Some remarks on etale homotopy theory and a conjecture of Adams, Topology 7 (1968), 111–116.Google Scholar
15.Quillen, D. G., The Adams conjecture, Topology 10 (1971), 67–80.Google Scholar
16.Quillen, D. G., The spectrum of an equivariant cohomology ring. I, II, Ann. of Math. (2) 94 (1971), 549–572; ibid. (2) 94 (1971), 573–602.CrossRefGoogle Scholar
17.Quillen, D. G., On the cohomology and K-theory of the general linear groups over a finite field, Ann. of Math. (2) 96 (1972), 552–586.Google Scholar
18.Quillen, D. G., Letter from Quillen to Milnor on Im(πi0 → πiS → KiZ), Algebraic K-theory (Proc. Conf., Northwestern Univ., Evanston, Ill., 1976), Springer, Berlin, 1976, pp. 182–188. Lecture Notes in Math. 551.Google Scholar
19.Sullivan, D., Genetics of homotopy theory and the Adams conjecture, Ann. of Math. (2) 100 (1974), 1–79.CrossRefGoogle Scholar
20.Whitehead, G. W., On the homotopy groups of spheres and rotation groups, Ann. of Math. (2) 43 (1942), 634–640.Google Scholar