Oli Jones

Artin groups with big outer automorphism groups

Artin groups are a rich class of groups generalising braid groups and closely connected to Coxeter groups. For each large-type triangle-free Artin group A, I will describe a contractible deformation space with an Out(A) action. This space is a useful tool for studying Out(A), especially when it is "big". I will discuss how to use this space to show that outer automorphism groups of such Artin groups are either virtually abelian, or contain a non-abelian free subgroup, and how to characterise this dichotomy in the Artin group's defining graph. I will then explain the conjectural picture of the structure of outer automorphism groups of large-type Artin groups. This talk is based on new results which appeared in my PhD thesis.