Let G 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 G 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 g≥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.
1
University of Copenhagen, Denmark
2
University of Southampton, UK
Dieter Degrijse; Nansen Petrosyan. Bredon cohomological dimensions for groups acting on $\mathrm{CAT}(0)$-spaces. Groups, geometry, and dynamics, Tome 9 (2015) no. 4, pp. 1231-1265. doi: 10.4171/ggd/339
@article{10_4171_ggd_339,
author = {Dieter Degrijse and Nansen Petrosyan},
title = {Bredon cohomological dimensions for groups acting on $\mathrm{CAT}(0)$-spaces},
journal = {Groups, geometry, and dynamics},
pages = {1231--1265},
year = {2015},
volume = {9},
number = {4},
doi = {10.4171/ggd/339},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/339/}
}
TY - JOUR
AU - Dieter Degrijse
AU - Nansen Petrosyan
TI - Bredon cohomological dimensions for groups acting on $\mathrm{CAT}(0)$-spaces
JO - Groups, geometry, and dynamics
PY - 2015
SP - 1231
EP - 1265
VL - 9
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/339/
DO - 10.4171/ggd/339
ID - 10_4171_ggd_339
ER -
%0 Journal Article
%A Dieter Degrijse
%A Nansen Petrosyan
%T Bredon cohomological dimensions for groups acting on $\mathrm{CAT}(0)$-spaces
%J Groups, geometry, and dynamics
%D 2015
%P 1231-1265
%V 9
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/339/
%R 10.4171/ggd/339
%F 10_4171_ggd_339
