# Questions tagged [fuchsian-groups]

In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R)

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### Critical exponent for groups with parabolics

I'm going to ask this question first in classical setting and then sketch its natural geometric setting. Let $\Gamma$ be a subgroup of $\operatorname{PSL}_2(\mathbb Z)$ (the question is mostly ...
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### Maximal orders and surface subgroups of even genus

Let $A$ be a quaternion algebra over a totally real number field $k$. Suppose that $A$ splits at exactly one real place of $A$. Let $\mathcal{O}$ be a maximal order in $A$. Then $\mathcal{O}$ contains ...
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### Almost modularity of Belyi curves and etale fundamental group of non-Belyi curves

Belyi's theorem states that every curve defined over $\mathbb{\bar Q}$ is almost modular (obtained from $\mathbb{H}^2/\Gamma,\ \Gamma$ a finite index subgroup of $PSL(2,\mathbb{Z})$), after ...
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### Regarding fundamental domain of 2 genus surface

Let $\mathbb{H}^2$ be the hyperbolic plane with $(2,3,7)$ tiling. Let $\Gamma$ be a subgroup of $(2,3,7)$ triangle group such that $\mathbb{H}^2/\Gamma$ is the compact orientable surface of genus 2 ...
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### Reference for triangle groups

Can anyone suggest to me some references for studying triangle groups? Especially the existence of finite index subgroups, subgroups isomorphic to fundamental groups of compact surfaces etc.
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