Complete Bredon cohomology and its applications to hierarchically defined groups

Abstract

By considering the Bredon analogue of complete cohomology of a group, we show that every group in the class \LHFF of type Bredon-\FP_\infty admits a finite dimensional model for \EFG. We also show that abelian-by-infinite cyclic groups admit a $3$-dimensional model for the classifying space for the family of virtually nilpotent subgroups. This allows us to prove that for \mF, the class of virtually cyclic groups, the class of \LHFF-groups contains all locally virtually soluble groups and all linear groups over $\mathbb C$ of integral characteristic.Comment: 14 page