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The principal bundle action in the Eilenberg-Moore spectral sequence

Published online by Cambridge University Press:  24 October 2008

W. D. Barcus
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Extract

In (2) the author determined a formula for computing, by means of the Eilenberg-Moore spectral sequence, the action of the group in a principal G-bundle, under the hypothesis that H*(G) be universally transgressively generated. This rather severe restriction was due to the method of proof, which used the theory of Guy Hirsch. Since Hirsch's work can be derived as a special case of Brown's twisted tensor products (3), one might hope to obtain the formula for the group action in the general case from the latter theory, and this we shall do (Theorem 1·2 below).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 87 - 93
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Adams, J. F. On the cobar construction. Colloque de topologie algérique (Louvain, 1956).Google Scholar
(2)Barcus, W. D.On the complexes of Hirsch and Eilenberg-Moore, Proc. Cambridge Philos. Soc. 64 (1968), 953–960.Google Scholar
(3)Brown, E. H. Jr. Twisted tensor products, I. Ann. of Math. 69 (1959), 223–246.CrossRefGoogle Scholar
(4)Eilenberg, S. and Moore, J. C.Homology and fibrations, I. Comment. Math. Helv. 40 (1966), 199–236.Google Scholar
(5)MacLane, S.Homology (Springer, Berlin, 1963).Google Scholar