The cluster symplectic double and moduli spaces of local systems

TL;DR

This paper proves a conjecture linking the cluster symplectic double to a moduli space of local systems, establishing a birational equivalence that advances understanding of their geometric relationship.

Contribution

It confirms a conjecture by Fock and Goncharov, establishing a birational equivalence between the cluster symplectic double and a moduli space of local systems.

Findings

Established a birational equivalence between the cluster symplectic double and a moduli space of local systems.

Proved a conjecture of Fock and Goncharov regarding their relationship.

Enhanced understanding of the geometric structures underlying cluster varieties and local systems.

Abstract

We prove a conjecture of Fock and Goncharov which provides a birational equivalence of a cluster variety called the cluster symplectic double and a certain moduli space of local systems associated to a surface.