A Functor Converting Equivariant Homology to Homotopy

Details A Functor Converting Equivariant Homology to Homotopy A Functor Converting Equivariant Homology to Homotopy

2006-03-18

arxiv.org/abs/math/0603455v2

Bulletin of the London Mathematical Society 2007 39(3): 499-508

Mathematics

Algebraic Topology

11 pages. Major style change. The final published version

Scientific paper

10.1112/blms/bdm029

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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