English

Labeled four cycles and the $K(\pi,1)$-conjecture for Artin groups

Group Theory 2024-10-31 v3 Geometric Topology Metric Geometry

Abstract

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

Keywords

Cite

@article{arxiv.2305.16847,
  title  = {Labeled four cycles and the $K(\pi,1)$-conjecture for Artin groups},
  author = {Jingyin Huang},
  journal= {arXiv preprint arXiv:2305.16847},
  year   = {2024}
}

Comments

Modifications according to the referee's report. Accepted version. 73 pages, 9 figures