When the outer automorphism groups of RAAGs are vast
Duration: 1 hour 2 mins
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Description: |
Sale, A (Vanderbilt University)
Thursday 12th January 2017 - 16:00 to 17:00 |
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Created: | 2017-02-01 16:03 |
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Collection: | Non-Positive Curvature Group Actions and Cohomology |
Publisher: | Isaac Newton Institute |
Copyright: | Sale, A |
Language: | eng (English) |
Distribution: | World (downloadable) |
Explicit content: | No |
Aspect Ratio: | 16:9 |
Screencast: | No |
Bumper: | UCS Default |
Trailer: | UCS Default |
Abstract: | 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.
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