Cluster braid groups of Coxeter-Dynkin diagrams
Journal of Combinatorial Theory, Series A(2024)
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 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.
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Key words
Braid groups,Cluster exchange groupoids,Coxeter-Dynkin diagrams,Generalized associahedron
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