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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The equivariant structure of Eilenberg-Mac Lane spaces. I. The $ {\bf Z}$-torsion free case

Author: Justin R. Smith
Journal: Proc. Amer. Math. Soc. 101 (1987), 731-737
MSC: Primary 55S91
MathSciNet review: 911042
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Abstract: The purpose of this paper is to continue the work begun in [7]. That paper described an obstruction theory for topologically realizing an (equivariant) chain-complex as the equivariant chain-complex of a CW-complex. The obstructions essentially turned out to be homological $ k$-invariants of Eilenberg-Mac Lane spaces and the key to their computation consists in developing tractable models for the chain-complexes of these spaces. The present paper constructs such a model in the $ {\mathbf{Z}}$-torsion free case. The model is sufficiently simple that in some cases it is possible to simply read off homological $ k$-invariants, and thereby derive some topological results.

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Keywords: Topological realization of chain-complexes, Steenrod problem, Eilenberg-Mac Lane spaces, bar construction
Article copyright: © Copyright 1987 American Mathematical Society