Quivers with potentials associated to triangulations of closed surfaces with at most two punctures (Q2099396)

The authors investigate the classification problem of nondegenerate potentials for quivers arising from triangulations of surfaces for the cases that remain left open. That is, for once-punctured closed surfaces of positive genus, the authors show that the quiver of any triangulation admits infinitely many nondegenerate potentials that are pairwise not weakly right-equivalent by showing that the potentials obtained by adding the 3-cycles coming from triangles and a fixed power of the cycle surrounding the puncture are well-behaved under flips and QP-mutations. For twice-punctured closed surfaces of positive genus, they prove that the quiver of any triangulation admits exactly one nondegenerate potential up to weak right-equivalence.