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Complete Bredon cohomology and its applications to hierarchically defined groups
Published online by Cambridge University Press: 08 April 2016
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
References
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