University College London, 03/09/2015
“The abelianization of automorphism groups of right-angled Artin groups”
Automorphism groups of right-angled Artin groups form an interesting class of groups, as they interpolate between the two extremal cases of Aut(F_n) and GL(n,Z). In this talk we will discuss some conditions on a simplicial graph which imply that the automorphism group of the associated right-angled Artin group has (in)finite abelianization. As a direct consequence, we obtain families of such automorphism groups that do not have Kazhdan’s property (T). This is joint work with Conchita Martinez-Perez.
“Coherence and fundamental groups of complex surfaces.”
A group is called coherent if all its finitely generated subgroups are finitely presented. I will describe a theorem due to Kapovich which provides a criterion for the fundamental group of a complex surface to be (in)coherent. Based on this criterion, we prove that certain Dehn fillings of non-uniform complex hyperbolic lattices are incoherent.
“Outer space for right-angled Artin groups.”
Automorphism groups of right-angled Artin groups generalize both GL(n,Z) and Out(F_n). Together with Ruth Charney we are developing an “outer space” which generalizes both the symmetric space for GL_n and the Outer space of a free group. I will discuss the current state of this project.