Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T14:36:35.616Z Has data issue: false hasContentIssue false
  • English
  • Français

Stable operations in mod p K-theory

Published online by Cambridge University Press:  24 October 2008

C. R. F. Maunder
C. R. F. Maunder
Affiliation:
Christ's College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Extract

There comes a time in the development of a cohomology theory when a discussion of cohomology operations becomes necessary. In the case of complex K-theory, the subject of the present paper, such operations have of course already been investigated by Adams (see (2)), so that any further discussion might appear superfluous. Powerful as Adams's results are, however, the situation still leaves something to be desired: it is not known just what other operations can be defined in K-theory, and it is an inconvenience from the standpoint of stable homotopy theory that Adams's operations are not themselves stable.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 3 , July 1967 , pp. 631 - 646
Copyright
Copyright © Cambridge Philosophical Society 1967

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 Chern characters and the structure of the unitary group. Proc. Cambridge Philos. Soc. 57 (1961), 189–199.CrossRefGoogle Scholar
(2)Adams, J. F.Vector fields on spheres. Ann. of Math. 75 (1962), 603–632.CrossRefGoogle Scholar
(3)Atiyah, M. F. and Hirzebruch, F. Vector bundles and homogeneous spaces. Proceedings of Symposia in Pure Mathematics, vol. III (American Mathematical Society; Providence, R.I., 1960), 7–38.Google Scholar
(4)Atiyah, M. F. and Hirzebruch, F.Analytic cycles on complex manifolds. Topology 1 (1962), 25–45.CrossRefGoogle Scholar
(5)Browder, W.Torsion in H-spaces. Ann. of Math. 74 (1961), 24–51.CrossRefGoogle Scholar
(6)Eilenberg, S. and Steenrod, N.Foundations of algebraic topology (Princeton, 1952).CrossRefGoogle Scholar
(7)Maunder, C. R. F.The spectral sequence of an extraordinary cohomology theory. Proc. Cambridge Philos. Soc. 59 (1963), 567–574.CrossRefGoogle Scholar
(8)Maunder, C. R. F.Mod p cohomology theories and the Bockstein spectral sequence. Proc. Cambridge Philos. Soc. 63 (1967), 23–43.CrossRefGoogle Scholar
(9)Milnor, J. W.The Steenrod algebra and its dual. Ann. of Math. 67 (1958), 150–171.CrossRefGoogle Scholar
(10)Milnor, J. W.On the cobordism ring Ω* and a complex analogue. Amer. J. Math. 82 (1960), 505–521.CrossRefGoogle Scholar
(11)Puppe, D.Homotopiemengen und ihre induzierten Abbildungen. I. Math. Z. 69 (1958), 199–244.Google Scholar
(12)Spanier, E. H.Function spaces and duality. Ann. of Math. 70 (1959), 338–378.CrossRefGoogle Scholar