On cluster algebras from once punctured closed surfaces

Abstract

We show that many cluster-theoretic properties of the Markov quiver hold also for adjacency quivers of triangulations of once-punctured closed surfaces of arbitrary genus. Along the way we consider the class P of quivers introduced by Kontsevich and Soibelman, characterize the mutation-finite quivers that belong to that class and draw some conclusions regarding non-degenerate potentials on them.

17 pages

References in corpus (5)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• The representation type of Jacobian algebras
• On Jacobian algebras from closed surfaces
• Mutation classes of certain quivers with potentials as derived equivalence classes
• Which mutation classes of quivers have constant number of arrows?

Cited by in corpus (6)

• A survey on maximal green sequences
• Maximal Green Sequences for Cluster Algebras Associated to the Orientable Surfaces of Genus n with Arbitrary Punctures
• Reddening Sequences for Banff Quivers and the Class $\mathcal{P}$
• From groups to clusters
• Quivers with potentials associated to triangulations of closed surfaces with at most two punctures
• Jacobian matrices of Y-seed mutations