# Tagged Questions

**3**

votes

**0**answers

109 views

### Criterion for a subgroup of $PSL_2(\mathbb R)$ to be Fuchsian

Let $\Gamma$ be a finitely generated subgroup of $PSL_2(\mathbb R)$.
I'm looking for effective criteria (idealy necessary and sufficient but just necessary would be a good start) ensuring that ...

**5**

votes

**1**answer

123 views

### Is the cardinality of occuring torsion subgroups in cofinite lattices in SL(2,R) bounded?

Let $\Gamma$ be a cofinite lattice in $PSL(2,\mathbb{R})$ with torsion subgroup $H$.
Is the a uniform bound on the cardinality of $H$?

**4**

votes

**1**answer

305 views

### Residual finiteness of fundamental groups of surfaces.

What is a simple way to prove that for any compact two-dimensional surface $S$ and an element $g$ in $\mathbb \pi_1(S)$ there exists a finite index normal subgroup $\Gamma\subset \pi_1(S)$ such that ...

**1**

vote

**3**answers

699 views

### Groups acting on Riemann Surfaces

By Hurwitz theorem, order of a group $G$ of automorphisms (conformal homeomorphisms) of a compact Riemann surface of genus $g\geq 2$ is bounded above by $84(g-1)$.
1. Is there any example of a ...

**10**

votes

**3**answers

661 views

### How do you recover the structure of the upper half plane from its description as a coset space?

This is maybe a dumb question. $SL_2(\mathbb{R})$ has a natural action on the upper half plane $\mathbb{H}$ which is transitive with stabilizer isomorphic to $SO_2(\mathbb{R})$. For this reason, ...