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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Pavel Tumarkin

Felikson, A., Shapiro, M. & Tumarkin, P. (2012). Cluster algebras and triangulated orbifolds. Advances in Mathematics 231(5): 2953-3002.

Author(s) from Durham


We construct geometric realizations for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston [10] to skew-symmetrizable case. Cluster variables for these algebras are renormalized lambda lengths on certain hyperbolic orbifolds. We also compute the growth rate of these cluster algebras, provide the positivity of Laurent expansions of cluster variables, and prove the sign-coherence of View the MathML source-vectors.