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 cluster exchange groupoid for any finite Coxeter-Dynkin diagram Δ and show that its fundamental group is isomorphic to the corresponding braid group associated with Δ.

中文翻译：

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Coxeter-Dynkin 图的簇辫子组


King-Qiu 引入簇交换群图作为簇交换图的增强，用于研究稳定性条件和二次微分。在本文中，我们介绍了任何有限 Coxeter-Dynkin 图 Δ 的簇交换群群，并证明其基本群与与 Δ 相关的相应辫子群同构。