Dimension invariants of outer automorphism groups

Recall that the geometric dimension $gd(G)$ of a group $G$ is the smallest dimension of a space on which $G$ acts in such a way that fixed point sets of finite subgroups are contractible. For many prominent classes of groups (e.g. for amenable groups, lattices in classical Lie groups, mapping class groups, groups of outer automorphisms of free groups...) one has equality between the geometric dimensions and the virtual cohomological dimension. On the other hand, there are some examples showing that these two notions of dimension might well differ. I will present some new examples of this phenomenon. This is joint work with Dieter Degrijse.