Videos

Hot Topics: Artin Groups and Arrangements - Topology, Geometry, and Combinatorics: "Artin groups and triangulated categories"

Presenter
March 13, 2024
Keywords:
  • Artin groups
  • braid groups
  • Coxeter groups
  • reflection groups
  • Garside structures
  • classifying spaces
  • hyperplane arrangements
  • subspace arrangements
  • configuration spaces
  • geometric group theory
  • Matroids
  • cohomology
MSC:
  • 14N20
  • 20F36
Abstract
In the last 30 years, geometric representation theory has produced a large stock of examples of linear 2-representations of Artin groups. These 2-representations have not really been used yet to prove genuinely new theorems about the groups themselves, but there is good reason to believe that they will eventually be useful to geometric group theorists. In the first part of this talk I will describe a simple example of a 2-representation of an Artin group, and explain how much of the classical theory of Artin groups is visible through it. In the latter part of the talk I will try to explain an approach to the K(\pi,1) conjecture which emerges from the study of spherical objects in this simple 2-representation.