Outer automorphisms of right-angled Coxeter groups

Tim Susse (Simon's Rock)

Abstract: We will discuss recent results on the structure of the outer automorphism group of a right-angled Coxeter group (RACG), comparing these with known results for the mapping class group, Out(F_n) and outer automorphism groups of RAAGs. We will show that outer automorphism groups of RACGs either large or virtually abelian, and give a condition on the definite graph that distinguishes these cases. As a consequence, this implies that Out of a RACG has property (T) if and only if it is finite. This is joint work with Andrew Sale.