Points of quantum SLn coming from quantumsnakes

We show that the quantized Fock-Goncharov monodromy matrices satisfy the relations of the quantum special linear group SL q n .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 SL n -quantum trace map for knots in thickened surfaces, partially developed in previous work of the author.20G42, 32G15, 57K31

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Publication Details

Journal
Algebraic & Geometric Topology
Published
2024-08-19
DOI
https://doi.org/10.2140/agt.2024.24.2537
Citations
2
Primary Topic
Algebraic structures and combinatorial models
Type
article
Field-Weighted Citation Impact
1.01
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article

Points of quantum SLn coming from quantumsnakes

Daniel C. Douglas
2 citations
Algebraic & Geometric Topology
Algebraic structures and combinatorial models
1.01
article

Points of quantum SLn coming from quantumsnakes

Daniel C. Douglas
article en
2 citations

Abstract

We show that the quantized Fock-Goncharov monodromy matrices satisfy the relations of the quantum special linear group SL q n .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 SL n -quantum trace map for knots in thickened surfaces, partially developed in previous work of the author.20G42, 32G15, 57K31

Algebraic & Geometric TopologyVol. 24(5)
Virginia Tech (US)
Openalex Percentile: Top 26%
Algebraic structures and combinatorial models
1.01
DOIOpen Access PDFOpenAlex
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Points of quantum SLn coming from quantumsnakes — Daniel C. Douglas · Algebraic & Geometric Topology (2024) | TGRS Research Map | TGRS