The equivariant structure of Eilenberg-Mac Lane spaces. I. The 𝑍-torsion free case

Smith, Justin R.

doi:10.1090/S0002-9939-1987-0911042-5

The equivariant structure of Eilenberg-Mac Lane spaces. I. The $\textbf {Z}$-torsion free case
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Proc. Amer. Math. Soc. 101 (1987), 731-737 Request permission

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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