A duality map for quantum cluster varieties from surfaces
Quantum Algebra
2019-04-30 v3 High Energy Physics - Theory
Geometric Topology
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.
Keywords
Cite
@article{arxiv.1509.01567,
title = {A duality map for quantum cluster varieties from surfaces},
author = {Dylan G. L. Allegretti and Hyun Kyu Kim},
journal= {arXiv preprint arXiv:1509.01567},
year = {2019}
}
Comments
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