### University of Arkansas Topology Seminar: 10/1/2015

### Speaker: Corey Bregman

### Title: Infinite groups acting faithfully on the outer automorphism group of a right-angled Artin group

Let Out(*G*) denote the outer automorphism
group of a group *G*. Out(*G*) provides a good measure of
the rigidity of *G*: if Out(*G*) is small, then almost every
symmetry of *G* is inner. A classical result of Hua−Reiner states
that Out(GL(*n*, ℤ)) is small, independent of *n*,
and work of Dyer−Formanek, Khramtsov and Bridson−Vogtmann has shown
that for the free group *F*_{n} with *n* > 2,
Out(Aut( *F*_{n})) and Out(Out *F*_{n})) are
trivial. We investigate Out(Out(*G*)) where *G* is a
general right-angled Artin group (raag). In contrast to the above, we
produce families of raags for which Out(Out(*G*)) contains
infinite projective ℤ−linear subgroups. This is joint
work with Neil Fullarton.

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