### The structure of automorphism groups of right-angled Artin groups

Algebra and Geometry Seminar

7th March 2018, 2:30 pm – 3:30 pm

Howard House, 4th Floor Seminar Room

A right-angled Artin group is a finitely presented group where every relation is a basic commutator of two of the generators. These groups include free groups and free abelian groups, and to some extent can be thought of as being built by gluing together free and free abelian groups. It is then natural to think of their automorphism groups as interpolating between $GL(n,mathbb{Z})$ and $Aut(F_n)$. In some recent work with Matthew Day, we give a more precise description of how this works. In particular, the the outer automorphism group has a finite index subgroup with a subnormal series where all of the consecutive quotients are either free abelian groups, copies of $GL(m,\mathbb{Z})$ for varying m, and 'F-R groups,' which are certain subgroups of automorphism groups of free products.

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