English

Bestvina metric and tree reduction for $K(\pi,1)$-conjecture

Group Theory 2026-02-23 v1 Geometric Topology Metric Geometry

Abstract

We reduce the K(π,1)K(\pi,1)-conjecture for all Artin groups to properties of Artin groups whose Coxeter diagrams are trees, from which we deduce new classes of Artin groups satisfying the K(π,1)K(\pi,1)-conjecture. This relies on constructing actions of Artin groups on Bestvina complexes of suitable Garside groupoids.

Keywords

Cite

@article{arxiv.2602.17982,
  title  = {Bestvina metric and tree reduction for $K(\pi,1)$-conjecture},
  author = {Jingyin Huang},
  journal= {arXiv preprint arXiv:2602.17982},
  year   = {2026}
}

Comments

50 pages, 5 figures