Hurwitz equivalence in the universal dihedral quandle
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910058359554048 |
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| author | Nakamura, Takuji Nakanishi, Yasutaka Satoh, Shin Wada, Kodai |
| author_facet | Nakamura, Takuji Nakanishi, Yasutaka Satoh, Shin Wada, Kodai |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11599 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hurwitz equivalence in the universal dihedral quandle Nakamura, Takuji Nakanishi, Yasutaka Satoh, Shin Wada, Kodai Geometric Topology Primary 20F36, 05E18, Secondary 57K12, 57M10 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. |
| title | Hurwitz equivalence in the universal dihedral quandle |
| topic | Geometric Topology Primary 20F36, 05E18, Secondary 57K12, 57M10 |
| url | https://arxiv.org/abs/2410.11599 |