On the expansion formulas of cluster varieties from surfaces and their combinatorial properties

Vu Tung Lam Dinh, Ivan Chi-Ho Ip

This paper explores the cluster algebra structure of the moduli space ${\mathcal{A}}_{{\mathrm{SL}}_{n+1},\mathbb{S}}$ of twisted ${\mathrm{SL}}_{n+1}$-local systems on a surface. We der…