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I will base my question on Fock and Goncharov's paper Dual Teichmüller and lamination spaces. Let $S$ be a surface with boundaries, marked points on such boundaries, punctures and boundaries without ...

Certain cluster algebras arise from ideal triangulations of hyperbolic Riemann surfaces. The combinatorics behind their mutations can be understood in terms of "flips" in the triangulation, and the ...

I am trying to understand the relations among Shear coordinates, lambda lengths, cluster variables, in the paper. Is the following correct? Lambda lengths = cluster A-variables Shear coordinates = ...