On finite quotients of surface braid groups having order at most $127$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915825353490432 |
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| author | Polizzi, Francesco Sabatino, Pietro |
| author_facet | Polizzi, Francesco Sabatino, Pietro |
| contents | Let $Σ_b$ be a compact Riemann surface of genus $b \geq 2$ and let $\mathsf{P}_2(Σ_b)=π_1(Σ_b \times Σ_b - Δ)$ be the corresponding pure braid group on two strands. A finite quotient $φ\colon \mathsf{P}_2(Σ_b) \to G$ is called "admissible" if $φ$ does not factor through $π_1(Σ_b \times Σ_b)$. In this work we classify all admissible quotients of $\mathsf{P}_2(Σ_b)$ such that $|G| \leq 127$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18817 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On finite quotients of surface braid groups having order at most $127$ Polizzi, Francesco Sabatino, Pietro Group Theory Algebraic Geometry Geometric Topology 20F36, 20D15, 05E16 Let $Σ_b$ be a compact Riemann surface of genus $b \geq 2$ and let $\mathsf{P}_2(Σ_b)=π_1(Σ_b \times Σ_b - Δ)$ be the corresponding pure braid group on two strands. A finite quotient $φ\colon \mathsf{P}_2(Σ_b) \to G$ is called "admissible" if $φ$ does not factor through $π_1(Σ_b \times Σ_b)$. In this work we classify all admissible quotients of $\mathsf{P}_2(Σ_b)$ such that $|G| \leq 127$. |
| title | On finite quotients of surface braid groups having order at most $127$ |
| topic | Group Theory Algebraic Geometry Geometric Topology 20F36, 20D15, 05E16 |
| url | https://arxiv.org/abs/2512.18817 |