Georgia Institute of Technology College of Sciences

Braid groups belong to a broad class of groups known as Artin groups, which are defined by presentations of a particular form and have played a major role in geometric group theory and low-dimensional topology in recent years. These groups fall into two classes, finite-type and infinte-type Artin groups. The former come equipped with a powerful combinatorial structure, known as a Garside structure, while the latter are much less understood and present many challenges. However, if one restricts to the Artin monoid, then much of the combinatorial structure still applies in the infinite-type case. In a joint project with Rachael Boyd, Rose Morris-Wright, and Sarah Rees, we use geometric techniques to study the relation between the Artin monoid and the Artin group.