Cluster braid groups of Coxeter-Dynkin diagrams

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 $\hat{I}”$ and show that the fundamental group of which is isomorphic to the corresponding braid group associated with $\hat{I}”$.

19 pages, 8 figures