Appears in collection : Higher Structures in Holomorphic and Topological Field Theory

Given a surface S, the moduli space of G-local systems on S equipped with a B-reduction and a T-framing at the boundary carries the structure of a cluster variety, by classic results of Fock and Goncharov. In essence, this means that there is a system of toric charts, and a compatible Poisson bracket, quadratic in each chart. Fock and Goncharov moreover quantized this structure by hand, giving rise to what they called a "quantum cluster ensemble".