Topology and Geometric Group Theory Seminar
Abstract: In the study of automorphisms of graph products of cyclic groups (including RAAGs and RACGs), a separating intersection of links (SIL) has been shown to hold a lot of power. The reason for this is that a SIL is exactly the necessary condition on the underlying graph that determines when two partial conjugations do not commute. We introduce two variations on a SIL that give a combinatorial condition on a right-angled Coxeter group that determine the dichotomy given in the title: the outer automorphism group of a RACG has a finite index subgroup that is either abelian or maps onto F2. This is joint work with Tim Susse.