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A Functor Converting Equivariant Homology to Homotopy

Zhaohu Nie
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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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BibTeXRIS

Zhaohu Nie. 2007-08-01. A Functor Converting Equivariant Homology to Homotopy. https://doi.org/10.1112/blms%2Fbdm029

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