Burau representation of braid groups and $q$-rationals
Geometric Topology
2023-09-11 v1 Combinatorics
Abstract
We establish a link between the new theory of -deformed rational numbers and the classical Burau representation of the braid group . We apply this link to the open problem of classification of faithful complex specializations of this representation. As a result we provide an answer to this problem in terms of the singular set of the -rationals and prove the faithfulness of the Burau representation specialized at complex outside the annulus
Keywords
Cite
@article{arxiv.2309.04240,
title = {Burau representation of braid groups and $q$-rationals},
author = {Sophie Morier-Genoud and Valentin Ovsienko and Alexander Veselov},
journal= {arXiv preprint arXiv:2309.04240},
year = {2023}
}