Work

Points of quantum SLn coming from quantum snakes

Year: 2024

Type: article

Abstract: We show that the quantized Fock-Goncharov monodromy matrices satisfy the relations of the quantum special linear group $\mathrm{SL}_n^q$. The proof employs a quantum version of the technology invented by Fock-Goncharov called snakes. This relationship between higher Teichmüller theory and quantum group theory is integral to the construction of a $\mathrm{SL}_n$-quantum trace map for knots in thickened surfaces, partially developed in a companion paper (arXiv:2101.06817).

Source: Algebraic & Geometric Topology

DOI: 10.2140/agt.2024.24.2537

Author: Daniel C Douglas

Institution: Virginia Tech

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: National Science Foundation

Awards: Character Varieties and Quantum Invariants, Classical and quantum homomorphisms from discrete groups to Lie groups