Singuläre definition der äquivarianten Bredon homologie

Abstract

Let G be a discrete group,o(G) the orbit category of G and M:o(G)→a a covariant (contravariant) functor to abelian groups. We define a singular equivariant homology theory H_*(X;M) (resp. H^*(X;M)) which satisfies a dimension axiom, in the sense of Bredon (Lecture notes 34). It turns out, that all fundamental properties of these theories directly follow by naturality from the analogous theorems in the classical non equivariant case.