Apparaît dans la collection : Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette

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.