Labeled four cycles and the K(π,1)-conjecture for Artin groups

2023/05/26 by Huang, Jingyin · 2 citations
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2305.16847

Abstract

We show that for a large class of Artin groups with Dynkin diagrams being a tree, the K(π,1)-conjecture holds. We also establish the K(π,1)-conjecture for another class of Artin groups whose Dynkin diagrams contain a cycle, which applies to some hyperbolic type Artin groups. This is based on a new approach to the K(π,1)-conjecture for Artin groups.

Cited by

• A new class of affine K(π,1) arrangements
• Normalisers of parabolic subgroups of Artin--Tits groups and Tits cone intersections

Related

• K(π,1) conjecture for Artin groups
• Cycles in spherical Deligne complexes and application to K(π,1)-conjecture for Artin groups
• Mini-Worskhop: Artin Groups meet Triangulated Categories
• K(π, 1)'s for Artin groups of finite type
• The dual approach to the K(π, 1) conjecture