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 Fn with n > 2, Out(Aut( Fn)) and Out(Out Fn)) 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.