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Complete Bredon cohomology and its applications to hierarchically defined groups

Published online by Cambridge University Press:  08 April 2016

BRITA E. A. NUCINKIS  and
NANSEN PETROSYAN
BRITA E. A. NUCINKIS
Affiliation:
Department of Mathematics, Royal Holloway, University of London, Egham, TW20 0EX. e-mail: [email protected]
NANSEN PETROSYAN
Affiliation:
School of Mathematics, University of Southampton, Southampton SO17 1BJ. e-mail: [email protected]
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Abstract

By considering the Bredon analogue of complete cohomology of a group, we show that every group in the class $\cll\clh^{\mathfrak F}{\mathfrak F}$ of type Bredon-FP∞ admits a finite dimensional model for $E_{\frak F}G$.

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 $\mathfrak {F}$, the class of virtually cyclic groups, the class of $\cll\clh^{\mathfrak F}{\mathfrak F}$-groups contains all locally virtually soluble groups and all linear groups over ${\mathbb{C}}$ of integral characteristic.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 161 , Issue 1 , July 2016 , pp. 143 - 156
Copyright
Copyright © Cambridge Philosophical Society 2016 

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