Karen Vogtmann - On the cohomological dimension of automorphism groups of RAAGs
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 22/12/2018

The  class  of  right-angled  Artin  groups  (RAAGs)  includes  free  groups  and free abelian groups, Both of these have extremely interesting automorphism groups, which share some properties and not others. We are interested in automorphism groups of general RAAGs,  and  in  particular  the  aspects  shared  with  automorphism  groups  of  free  groups.
These aspects are captured by the subgroup of untwisted automorphisms. For free groups, the  virtual  cohomological  dimension  of  the  automorphism  group  is  equal  to  the  rank  of
a maximal free abelian subgroup. We conjecture that the same is true for the untwisted subgroup for general RAAGs, and prove this in many cases. The idea is to construct abelian subgroups that closely mirror the structure of a space with a proper cocompact action. This talk is based on joint work with Ruth Charney and with Ben Millard.