Finite quotients of Fuchsian groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929561401294848 |
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| author | Chan, Frankie Styron, Lindsey |
| author_facet | Chan, Frankie Styron, Lindsey |
| contents | This work provides an effective algorithm for distinguishing finite quotients between two non-isomorphic finitely generated Fuchsian groups $Γ$ and $Λ$. It will suffice to take a finite quotient which is abelian, dihedral, a subgroup of $\mathrm{PSL}(2,\mathbf{F}_q)$, or an abelian extension of one of these 3. We will develop an approach for creating group extensions upon a shared finite quotient of $Γ$ and $Λ$ which between them have differing degrees of smoothness. Regarding the order of a finite quotient that distinguishes between $Γ$ and $Λ$, we establish an upperbound as a function of the genera, the number of punctures, and the cone orders arising in $Γ$ and $Λ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20329 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite quotients of Fuchsian groups Chan, Frankie Styron, Lindsey Group Theory Geometric Topology This work provides an effective algorithm for distinguishing finite quotients between two non-isomorphic finitely generated Fuchsian groups $Γ$ and $Λ$. It will suffice to take a finite quotient which is abelian, dihedral, a subgroup of $\mathrm{PSL}(2,\mathbf{F}_q)$, or an abelian extension of one of these 3. We will develop an approach for creating group extensions upon a shared finite quotient of $Γ$ and $Λ$ which between them have differing degrees of smoothness. Regarding the order of a finite quotient that distinguishes between $Γ$ and $Λ$, we establish an upperbound as a function of the genera, the number of punctures, and the cone orders arising in $Γ$ and $Λ$. |
| title | Finite quotients of Fuchsian groups |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2410.20329 |