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arXiv · 1402.2134

Complete Bredon cohomology and its applications to hierarchically defined groups

Brita E. A. Nucinkis·Nansen Petrosyan
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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.

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Brita E. A. Nucinkis, Nansen Petrosyan. 2014-02-10. Complete Bredon cohomology and its applications to hierarchically defined groups. https://doi.org/10.1017/s0305004116000190

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