Floer potentials, cluster algebras and quiver representations

TL;DR

This paper links Floer potentials of monotone Lagrangian tori in toric del Pezzo surfaces to cluster algebras and quiver representations, providing a new interpretative framework.

Contribution

It introduces a novel interpretation of Floer potentials as cluster characters of quiver representations using cluster algebras.

Findings

Floer potentials are interpreted via cluster characters.

Cluster algebras provide a new perspective on Lagrangian tori.

The approach connects symplectic geometry with algebraic combinatorics.

Abstract

We use cluster algebras to interpret Floer potentials of monotone Lagrangian tori in toric del Pezzo surfaces as cluster characters of quiver representations.