Cohomological dimension of Mackey functors for infinite groups

Abstract

We consider the cohomology of Mackey functors for infinite groups and define the Mackey-cohomological dimension cd G of a group G. We will relate this dimension to other cohomological dimensions such as the Bredon-cohomological dimension cdG and the relative cohomological dimension -cdG. In particular, we show that for virtually torsion free groups the Mackeycohomological dimension is equal to both -cdG and the virtual cohomological dimension. © 2006 London Mathematical Society.