A duality map for quantum cluster varieties from surfaces

Abstract

We define a canonical map from a certain space of laminations on a punctured surface into the quantized algebra of functions on a cluster variety. We show that this map satisfies a number of special properties conjectured by Fock and Goncharov. Our construction is based on the "quantum trace" map introduced by Bonahon and Wong. (C) 2016 Elsevier Inc. All rights reserved.