Hostname: page-component-6766d58669-tq7bh Total loading time: 0 Render date: 2026-05-22T20:27:53.030Z Has data issue: false hasContentIssue false
  • English
  • Français

Mod p cohomology theories and the Bockstein spectral sequence

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

Introduction. Let h*(X, A) be an extraordinary cohomology theory defined on the category of finite CW-pairs, that is, a cohomology theory satisfying all the axioms of Eilenberg and Steenrod (7) except the dimension axiom. This paper has three objects: to define and investigate the properties of the associated mod p cohomology theory h*(X, A; Zp) (see also (9)), to show that (with certain restrictions) if h*(X, A) is a multiplicative cohomology theory, so is h*(X, A. Zp), and lastly to generalize the notion of Bockstein coboundary homomorphisms and the apparatus of the Bockstein spectral sequence (see (4)) to an extraordinary cohomology theory.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 1 , January 1967 , pp. 23 - 43
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.)

Article purchase

Temporarily unavailable

References

REFERENCES

(1)Atiyah, M. F.Vector bundles and the Künneth formula. Topology 1 (1962), 245–248.CrossRefGoogle Scholar
(2)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), pp. 7–38.Google Scholar
(3)Barratt, M. G.Track groups. II. Proc. London Math. Soc. (3) 5 (1957), 285–329.Google Scholar
(4)Browder, W.Torsion in H-spaces. Ann. of Math. 74 (1961), 24–51.CrossRefGoogle Scholar
(5)Brown, E. H.Cohomology theories. Ann. of Math. 75 (1962), 467–484.CrossRefGoogle Scholar
(6)Dold, A. Relations between ordinary and extraordinary homology. Colloquium on Algebraic Topology, Aarhus, 1962 (mimeographed notes), pp. 2–9.Google Scholar
(7)Eilenberg, S. and Steenrod, N.Foundations of algebraic topology. (Princeton, 1952.)CrossRefGoogle Scholar
(8)Maunder, C. R. F.Cohomology operations of the Nth. kind. Proc. London Math. Soc. (3) 13 (1963), 125–154.CrossRefGoogle Scholar
(9)Maunder, C. R. F.Stable operations in mod p K-theory. Proc. Cambridge Philos. Soc. (to appear).Google Scholar
(10)Puppe, D.Homotopiemengen und ihre induzierten Abbildungen. I. Math. Z. 69 (1958), 199–244.Google Scholar
(11)Whitehead, G. W.Generalized homology theories. Trans. Amer. Math. Soc. 102 (1962), 227–283.CrossRefGoogle Scholar