Cluster algebras and triangulated orbifolds

Understand

We construct geometric realization for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston to skew-symmetrizable case.

• Cluster variables for these algebras are renormalized lambda lengths on certain hyperbolic orbifolds.
• We also compute growth rate of these cluster algebras, provide positivity of Laurent expansions of cluster variables, and prove sign-coherence of c-vectors.