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Generalized Eilenberg–Moore spectral sequences for elementary abelian groups and tori

Published online by Cambridge University Press:  24 October 2008

J. P. C. Greenlees
J. P. C. Greenlees
Affiliation:
Department of Mathematics, University of Sheffield, The Hicks Building, Sheffield, S3 7RH
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Abstract

In this note we prove universal coefficient theorems for Borel cohomology and related theories. Whatever other merit this may have the comment of Borel [5] applies ‘ …elle a au moms l'utilité de bien mettre en évidence le rôle fondamental joué dans cette question par la cohomologie des groupes’.

Indeed the purpose of the enterprise is to use homological properties of the group cohomology ring H*(BG+) to study properties of G-spaces. Because of the relative simplicity of ordinary cohomology much attention in the proofs and applications is concentrated on change of groups, and on changes in the way the group action is exploited. Nonetheless we are able to adapt the non-equivariant approach of Adams ([1, 2]; see also [3]). Thus the existence of universal coefficient theorems automatically gives Kiinneth theorems as special cases.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 1 , July 1992 , pp. 77 - 89
Copyright
Copyright © Cambridge Philosophical Society 1992

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