Artin groups are a broad class of groups whose presentations all follow a particular pattern. They are generalizations of braid groups and are closely related to Coxeter groups. Artin groups provide examples of groups with many interesting properties but there is very little that is known about ALL Artin groups.
In the first lecture, we’ll define Artin groups, talk about different types of Artin groups, and give a summary of known results and open questions. In the second lecture, we’ll focus on algebraic techniques for studying Artin groups, including the Garside structure, parabolic subgroups, and, if time permits, the Artin monoid. In the third lecture, we’ll discuss geometric techniques for studying Artin groups, including the Deligne complex and newer complexes such as the Clique-cube complex and the systolic Artin complex.
These videos were part of the Geometric group theory without boundaries II virtual summer school.
