Points of quantum $\mathrm{SL}_n$ coming from quantum snakes
Geometric Topology
2025-02-12 v3 Quantum Algebra
Abstract
We show that the quantized Fock-Goncharov monodromy matrices satisfy the relations of the quantum special linear group . The proof employs a quantum version of the technology invented by Fock-Goncharov called snakes. This relationship between higher Teichm\"uller theory and quantum group theory is integral to the construction of a -quantum trace map for knots in thickened surfaces, partially developed in a companion paper (arXiv:2101.06817).
Cite
@article{arxiv.2103.04471,
title = {Points of quantum $\mathrm{SL}_n$ coming from quantum snakes},
author = {Daniel C. Douglas},
journal= {arXiv preprint arXiv:2103.04471},
year = {2025}
}
Comments
47 pages (double-spaced), 21 figures. Version 3: Final version after publication