# Questions tagged [fuchsian-groups]

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

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### Equations defining hyperbolic geodesics in $\mathbb C \setminus\{0,1\}$

Let $X=\mathbb C\setminus\{0,1\}$, equipped with the hyperbolic structure it inherits from Klein's modular $\lambda$ function $\lambda:\mathbb H \to X$. In each (non-peripheral and nontrivial) free-...
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### Positive genus Fuchsian groups

Let $G$ be a lattice in $SL(2,\mathbb{R})$. Is it always true that there exists a finite index subgroup $F$ of $G$ such that the quotient surface $\mathbb{H}/F$ has positive genus? Is the statement ...
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### Fuchsian groups and Eichler's result

Let $G$ be a Fuchsian group of first kind contained in $\text{PSL}_2(\mathbb{R})$. A result of Eichler says, there exists a finite set $S\subset G$ such that any $\gamma$ in $G$ can be written as a ...
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### Reference for openness of subspace of PSL(2,R) representation variety corresponding to Teichmuller space

Let $S$ be a compact oriented surface with nonempty boundary. There are two variants of Teichmuller space for $S$ you might consider: The one that parameterizes finite-volume complete hyperbolic ...
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### Conjugate Groups of (quasi) Fuchsian Groups

I apologize in advance if this question is so trivial or too low level. Let $\Gamma$ be a Fuchsian group. Let $\mathcal{F}$ be the set of pairs $(\mu,f)$, where $\mu \in L^\infty(\mathbb{C})$ such ...
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