Hurwitz equivalence in the universal dihedral quandle

Takuji Nakamura; Yasutaka Nakanishi; Shin Satoh; Kodai Wada

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arXiv · 2410.11599

Hurwitz equivalence in the universal dihedral quandle

Takuji Nakamura·Yasutaka Nakanishi·Shin Satoh·Kodai Wada

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Abstract

We investigate the Hurwitz action of the $m$-braid group on the $m$-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 $m$-braid group, the virtual $m$-braid group, and the virtual pure $m$-braid group.

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Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh, Kodai Wada. 2024-10-15. Hurwitz equivalence in the universal dihedral quandle. https://arxiv.org/abs/2410.11599

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