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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > When the outer automorphism groups of RAAGs are vast

## When the outer automorphism groups of RAAGs are vastAdd to your list(s) Download to your calendar using vCal - Andrew Sale (Vanderbilt University)
- Thursday 12 January 2017, 16:00-17:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact INI IT. NPCW01 - Non-positive curvature in action The outer automorphism groups of right-angled Artin groups (RAAGs) give a way to build a bridge between GL(n,Z) and Out(Fn). We will investigate certain properties of these groups which could be described as “vastness” properties, and ask if it possible to build a boundary between those which are “vast” and those which are not. One such property is as follows: given a group G, we say G has all finite groups involved if for each finite group H there is a finite index subgroup of G which admits a map onto H. From the subgroup congruence property, it is known that the groups GL(n,Z) do not have every finite group involved for n>2. Meanwhile, the representations of Out(Fn) given by Grunewald and Lubotzky imply that these groups do have all finite groups involved. We will describe conditions on the defining graph of a RAAG that are necessary and sufficient to determine when it's outer automorphism group has this property. The same criterion also holds for other properties, such as SQ-universality, or having a finite index subgroup with infinite dimensional second bounded cohomology. This is joint work with V. Guirardel. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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