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An equivariant version of the Kuhn–Schwartz non-realizability theorem

Published online by Cambridge University Press:  26 July 2002

DORRA BOURGUIBA  and
DAGMAR M. MEYER
DORRA BOURGUIBA
Affiliation:
Faculté de Sciences–Mathématiques, Université de Tunis, 1060 Tunis, Tunisia. e-mail: [email protected]
DAGMAR M. MEYER
Affiliation:
LAGA, Institut Galilée, Université Paris 13, 93430 Villetaneuse, France. e-mail: [email protected]
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Abstract

The Kuhn–Schwartz non-realizability theorem states the following: if the mod p cohomology of a topological space is finitely generated as a module over the Steenrod algebra [Ascr ] then it is finite. We generalize this result to the category of G-spaces, where G is a compact Lie group, by considering the equivariant cohomology of a G-space as an object in the category of all [Ascr ]-modules with a compatible H*(BG; [ ]p)-module structure.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 133 , Issue 1 , July 2002 , pp. 117 - 124
Copyright
2002 Cambridge Philosophical Society

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