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.

40 pages. Version 2: Removed unjustified assertions about positivity and corrected proofs. Version 3: Listed author affiliations upon request of the second author's institute

References in corpus (1)

• The quantum dilogarithm and representations quantum cluster varieties

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