- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:01
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
9
2015
4
Bredon cohomological dimensions for groups acting on CAT(0)-spaces
Dieter
Degrijse
University of Copenhagen, COPENHAGEN Ø, DENMARK
Nansen
Petrosyan
University of Southampton, SOUTHAMPTON, UNITED KINGDOM
Bredon cohomological dimension, discrete actions, CAT(0)-spaces
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 fi nite 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.
$K$-theory
Nonassociative rings and algebras
1231
1265
10.4171/GGD/339
http://www.ems-ph.org/doi/10.4171/GGD/339