- journal article metadata
European Mathematical Society Publishing House
2017-12-10 23:40:02
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
11
2017
4
Dimension invariants of outer automorphism groups
Dieter
Degrijse
National University of Ireland, Galway, Ireland
Juan
Souto
Université de Rennes 1, France
Outer automorphism groups, geometric dimension for proper actions, virtual cohomological dimension
The geometric dimension for proper actions $\underline{\mathrm{gd}}(G)$ of a group $G$ is the minimal dimension of a classifying space for proper actions $\underline{E}G$. We construct for every integer $r\geq 1$, an example of a virtually torsion-free Gromov-hyperbolic group $G$ such that for every group $\Gamma$ which contains $G$ as a finite index normal subgroup, the virtual cohomological dimension vcd$(\Gamma)$ of $\Gamma$ equals $\underline{\mathrm{gd}}(\Gamma)$ but such that the outer automorphism group Out$(G)$ is virtually torsion-free, admits a cocompact model for $\underline{E}$ Out$(G)$ but nonetheless has vcd(Out$(G))\le \underline{\mathrm{gd}}$(Out$(G))-r$.
Group theory and generalizations
1469
1495
10.4171/GGD/435
http://www.ems-ph.org/doi/10.4171/GGD/435
12
7
2017