Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T08:41:39.649Z Has data issue: false hasContentIssue false
  • English
  • Français

The infinite loop Adams conjecture via classification theorems for ℱ-spaces

Published online by Cambridge University Press:  24 October 2008

Eric M. Friedlander
Eric M. Friedlander
Affiliation:
Northwestern University, Evanston, Illinois 60201
Get access Rights & Permissions [Opens in a new window]

Extract

We prove the following generalized version of the complex Adams conjecture (see Theorem 10·4), as announced in (5).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 1 , January 1980 , pp. 109 - 150
Copyright
Copyright © Cambridge Philosophical Society 1980

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)Artin, M. and Mazur, B. Etale homotopy. Lecture Notes in Mathematics, no. 100 (Berlin, Springer-Verlag, 1969).Google Scholar
(2)Bousfield, A. K. and Friedlander, E. M. Homotopy theory of Γ-spaces, spectra, and bisimplicial sets. Lecture Notes in Mathematics, no. 658 (Berlin, Springer-Verlag, 1978), pp. 80–130.Google Scholar
(3)Bousfield, A. K. and Kan, D. M. Homotopy limits, completions, and localizations. Lecture Notes in Mathematics, no. 304 (Berlin, Springer-Verlag, 1972).Google Scholar
(4)Friedlander, E. M.Computations of K-theories of finite fields. Topology 10 (1975), 87–109.Google Scholar
(5)Friedlakder, E. M. and Seymour, R.Two proofs of the Stable Adams Conjecture. Bull. Amer. Math. Soc. 83 (1977), 1300–1302.Google Scholar
(6)Gabriel, P. and Zisman, M. Calculus of fractions and homotopy theory. Ergebn. Math. 34 (Springer, 1967).Google Scholar
(7)Hoobler, R. and Rector, D. L. Arithmetic K-theory. Lecture Notes in Mathematics, no. 418 (Berlin, Springer-Verlag, 1974), pp. 78–95.Google Scholar
(8)Maclane, S.Categories for the working mathematician. Grad. Texts in Math. 5 (Berlin, Springer-Verlag, 1971).Google Scholar
(9)May, J. P.Classifying spaces and fibrations. Mem. Amer. Math. Soc. 1, issue 1, no. 155 (1975).Google Scholar
(10)May, J. P.E ∞ ring spaces and E ∞ ring spectra. Lecture Notes in Mathematics, no. 577 (Berlin, Springer-Verlag, 1977).Google Scholar
(11)May, J. P.The spectra associated to permutative categories. Topology, 17 (1978), 225–228.CrossRefGoogle Scholar
(12)May, J. P.The spectra associated to ℐ-monoids. Proc. Cambridge Philos. Soc. 84 (1978), 313–322.CrossRefGoogle Scholar
(13)Quillen, D. Homotopical algebra. Lecture Notes in Mathematics, no. 43 (Berlin, Springer-Verlag, 1967).Google Scholar
(14)Quillen, D.Geometric realization of a Kan fibration is a Serre fibration. Proc. Amer. Math. Soc. 19 (1968), 1499–1500.Google Scholar
(15)Segal, G.Categories and cohomology theories. Topology 13 (1974), 293–312.CrossRefGoogle Scholar
(16)Sullivan, D.Genetics of homotopy theory and the Adams conjecture. Ann. of Math. 100 (1974), 1–79.Google Scholar