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A Functor Converting Equivariant Homology to Homotopy

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Published Article
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DOI: 10.1112/blms/bdm029
arXiv ID: math/0603455
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arXiv
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Abstract

In this paper, we prove an equivariant version of the classical Dold-Thom theorem. Associated to a finite group, a CW-complex on which this group acts and a covariant coefficient system in the sense of Bredon, we functorially construct a topological abelian group by the coend construction. Then we prove that the homotopy groups of this topological abelian group are naturally isomorphic to the Bredon equivariant homology of the CW-complex. At the end we present several examples of this result.

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