Knots and Coxeter Groups
Geometric Topology
2025-03-17 v1
Abstract
In this paper we study knots created by galleries in the affine Coxeter complex of type \widewedge{B3}. We bound the stick number by 40 and prove that the smallest length of threefold rotationally symmetric trefoils is 42. We construct explicit galleries that knot as 9_35, 9_40, 9_41 and 9_47 in a way that has threefold rotational symmetry. We explain the construction of these galleries for 9_47 carefully. We conclude with three questions inspired by this work.
Cite
@article{arxiv.2503.10785,
title = {Knots and Coxeter Groups},
author = {Dylan Burke and Geoffrey Cuff-Chartrand and Malors Espinosa and Mateusz Kazimierczak and Mohammadamin Mobedi},
journal= {arXiv preprint arXiv:2503.10785},
year = {2025}
}