2017/12/20 by Nansen Petrosyan, Petrosyan, Nansen, Tomasz Prytuła +1
Mathematics · #05E18 #05E45 (Primary) 20E08 #20F65 #20J06 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #math.AT #math.GR #msc:05E18 #msc:05E45 #msc:20E08 #msc:20F65 #msc:20J06
paper · pdf · doi:10.48550/arxiv.1712.07606
24 pages, 6 figures. In Theorem 1.2 the assumption that the action on the building is minimal is removed as it always holds. This is shown in Lemma 5.1
arxiv created 2018/02/21 · arxiv updated 2018/02/23
We consider a strictly developable simple complex of finite groups G(\mathcal Q). We show that Bestvina's construction for Coxeter groups applies in this more general setting to produce a complex that is equivariantly homotopy equivalent to the standard development. When G(\mathcal Q) is non-positively curved, this implies that the Bestvina complex is a cocompact classifying space for proper actions of G of minimal dimension. As an application, we show that for groups that act properly and chamber transitively on a building of type (W, S), the dimension of the associated Bestvina complex is the virtual cohomological dimension of W. We give further examples and applications in the context of Coxeter groups, graph products of finite groups, locally 6-large complexes of groups and groups of rational cohomological dimension at most one. Our calculations indicate that, because of its minimal cell structure, the Bestvina complex is well-suited for cohomological computations.