JournalsggdVol. 9, No. 4pp. 1231–1265

Bredon cohomological dimensions for groups acting on CAT(0)-spaces

  • Dieter Degrijse

    University of Copenhagen, Denmark
  • Nansen Petrosyan

    University of Southampton, UK
Bredon cohomological dimensions for groups acting on CAT(0)-spaces cover
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Abstract

Let GG be a group acting isometrically with discrete orbits on a separable complete CAT(0)-space of bounded topological dimension. Under certain conditions, we give upper bounds for the Bredon cohomological dimension of GG for the families of finite and virtually cyclic subgroups. As an application, we prove that the mapping class group of any closed, connected, and orientable surface of genus g2g ≥ 2 admits a $9g-8)-dimensional classifying space with virtually cyclic stabilizers. In addition, our results apply to fundamental groups of graphs of groups and groups acting on Euclidean buildings. In particular, we show that all finitely generated linear groups of positive characteristic have a finite dimensional classifying space for proper actions and a finite dimensional classifying space for the family of virtually cyclic subgroups. We also show that every generalized Baumslag–Solitar group has a 3-dimensional model for the classifying space with virtually cyclic stabilizers.

Cite this article

Dieter Degrijse, Nansen Petrosyan, Bredon cohomological dimensions for groups acting on CAT(0)-spaces. Groups Geom. Dyn. 9 (2015), no. 4, pp. 1231–1265

DOI 10.4171/GGD/339