Hot Topics: Artin Groups and Arrangements - Topology, Geometry, and Combinatorics: "K(π, 1)-conjecture for Artin groups via combinatorial non-positive curvature"
Presenter
March 14, 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
We establish a close connection between simple properties about 4-cycles in certain graphs and the K(pi,1)-conjecture, via elements of non-positively curvature geometry. We also propose a new approach for studying this conjecture. As a consequence, we deduce many new cases of Artin groups which satisfies the K(pi,1)-conjecture. If time allows, I will also discuss a connections between K(pi,1)-conjecture for Artin groups and finding certain types of sub-arrangements inside the deconing of arrangements associated with finite Coxeter groups.