Hurwitz equivalence in the universal dihedral quandle
Geometric Topology
2026-03-20 v2
Abstract
We investigate the Hurwitz action of the -braid group on the -fold Cartesian product of the universal dihedral quandle. We introduce three computable invariants and prove that they give a complete classification of the orbits under this action. As a consequence, we describe an explicit complete system of orbit representatives. We further obtain analogous classifications for the corresponding Hurwitz actions of the pure -braid group, the virtual -braid group, and the virtual pure -braid group.
Cite
@article{arxiv.2410.11599,
title = {Hurwitz equivalence in the universal dihedral quandle},
author = {Takuji Nakamura and Yasutaka Nakanishi and Shin Satoh and Kodai Wada},
journal= {arXiv preprint arXiv:2410.11599},
year = {2026}
}
Comments
22 pages. The original manuscript has been split into two separate papers. This version (v2) contains the first part; the second part will appear as a separate submission