Quivers with potentials associated to triangulations of closed surfaces with at most two punctures
type: Item
instance of: scholarly article
title: Quivers with potentials associated to triangulations of closed surfaces with at most two punctures
author: Jan Geuenich
author: Daniel Labardini-Fragoso
author: José Luis Miranda-Olvera
published in: Séminaire Lotharingien de Combinatoire
publication date: 2022-11-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/2008.10168
full work available at URL: s84geuen.html
review text: 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.
reviewed by: Mee Seong Im
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 05E16
Mathematics Subject Classification ID: 13F60
zbMATH DE Number: 7622547
zbMATH Keywords: surface
zbMATH Keywords: marked points
zbMATH Keywords: punctures
zbMATH Keywords: triangulation
zbMATH Keywords: flip
zbMATH Keywords: quiver
zbMATH Keywords: potential
zbMATH Keywords: mutation
zbMATH Keywords: non-degenerate potential
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7622547