Abstract
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We show that the quantized Fock–Goncharov monodromy
matrices satisfy the relations of the quantum special linear group
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The proof employs a quantum version of the technology of Fock and
Goncharov, called snakes. This relationship between higher Teichmüller
theory and quantum group theory is integral to the construction of an
–quantum
trace map for knots in thickened surfaces, partially developed in previous work of the
author.
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Keywords
quantum trace map, Fock–Goncharov coordinates
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Mathematical Subject Classification
Primary: 20G42, 32G15, 57K31
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Publication
Received: 14 August 2021
Revised: 3 June 2023
Accepted: 26 June 2023
Published: 19 August 2024
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| © 2024 MSP (Mathematical Sciences
Publishers). Distributed under the Creative Commons
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