English

Cluster braid groups of Coxeter-Dynkin diagrams

Combinatorics 2023-10-23 v2 Geometric Topology Representation Theory

Abstract

Cluster exchange groupoids are introduced by King-Qiu as an enhancement of cluster exchange graphs to study stability conditions and quadratic differentials. In this paper, we introduce the exchange groupoid for any finite Coxeter-Dynkin diagram Δ\Delta and show that the fundamental group of which is isomorphic to the corresponding braid group associated with Δ\Delta.

Keywords

Cite

@article{arxiv.2310.02871,
  title  = {Cluster braid groups of Coxeter-Dynkin diagrams},
  author = {Zhe Han and Ping He and Yu Qiu},
  journal= {arXiv preprint arXiv:2310.02871},
  year   = {2023}
}

Comments

19 pages, 8 figures

R2 v1 2026-06-28T12:40:30.258Z