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arxiv: 1509.01567 · v3 · pith:T23VLPMNnew · submitted 2015-09-04 · 🧮 math.QA · hep-th· math.GT

A duality map for quantum cluster varieties from surfaces

Dylan G. L. Allegretti , Hyun Kyu Kim This is my paper
classification 🧮 math.QA hep-thmath.GT
keywords clusterquantumalgebrabonahoncanonicalcertainconjecturedconstruction
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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.

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  1. Quantized Geodesic Lengths for Teichm\"uller Spaces: Algebraic Aspects

    math.GT 2024-05 unverdicted novelty 5.0

    Constructs quantized trace-of-monodromy via Bonahon-Wong maps and verifies Teschner recursion plus strong commutation for disjoint loops in Chekhov-Fock quantum Teichmüller theory.