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

• 成果类型: Article
• 署名作者: Huang, Jingyin
• 署名单位: University System of Ohio; Ohio State University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01294-w
• 发表日期: 2024
• 页码: 905-994
• 关键词: parabolic subgroups; tits groups; hyperplane complements; spherical-type; k(pi; arrangements; lattices; TOPOLOGY

摘要

We show that for a large class of Artin groups with Dynkin diagrams being a tree, the K(pi,1)-conjecture holds. We also establish the K(pi,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(pi,1)-conjecture for Artin groups.