On Dimensions in Bredon Homology

B. E. A. Nucinkis

We shall define a homological and cohomological dimension of groups in the context of Bredon homology and compare the two quantities. We shall apply this to describe the Bredon-homological dimension of nilpotent groups in terms of the Hirsch-rank. In particular this implies that for virtually torsion-free nilpotent groups the Bredon cohomological dimension is equal to the virtual cohomological dimension.