Complete Bredon cohomology and its applications to hierarchically defined groups

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 C of integral characteristic.

10.1017/S0305004116000190

0305-0041

143-156

Nucinkis, Brita

86582f48-4da6-4868-8700-d16ea4236c86

Petrosyan, Nansen

f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6

Nucinkis, Brita

86582f48-4da6-4868-8700-d16ea4236c86

Petrosyan, Nansen

f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6

Nucinkis, Brita and Petrosyan, Nansen (2016) Complete Bredon cohomology and its applications to hierarchically defined groups. Mathematical Proceedings of the Cambridge Philosophical Society, 161 (1), 143-156. (doi:10.1017/S0305004116000190).

Record type: Article

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 C of integral characteristic.