arXiv 1402.21342014-02-10math.GRmath.AT

Complete Bredon cohomology and its applications to hierarchically defined groups

Brita E. A. Nucinkis, Nansen Petrosyan

备注：: 14 pages
发表信息：: Math. Proc. Camb. Phil. Soc. 161 (2016) 143-156
DOI：: 10.1017/S0305004116000190

英文摘要：

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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