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arXiv · 2310.02871

Cluster braid groups of Coxeter-Dynkin diagrams

Zhe Han·Ping He·Yu Qiu
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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 $Δ$ and show that the fundamental group of which is isomorphic to the corresponding braid group associated with $Δ$.

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Zhe Han, Ping He, Yu Qiu. 2023-10-20. Cluster braid groups of Coxeter-Dynkin diagrams. https://arxiv.org/abs/2310.02871

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