Hecke Functors and the Equivariant Dold-Thom Theorem

Abstract

We recall that the Dold-Thom theorem [3] asserts that the weak homotopy type cf a topological abelian group is determined by its homotopy groups, and hence the homotopy category cf topological abelian groups with respect to weak equivalences is equivalent to the category cf graded abelian groups. In this note we consider the equivariant version. We restrict ourself to the case cf finite group actions. Let G be a finite group, and let k be a commutative ring with unit. A topological &[G]module is a topological abelian group M as well as a &[G]-module such that the bilinear map