1
$\begingroup$

Let $B$ be a finite set in $\mathbf{P}^1(\mathbf{C})$. Let $G$ be the fundamental group of $\mathbf{P}^1(\mathbf{C}) - B$.

We can view $G$ as a subgroup of $\mathrm{SL}_2(\mathbf{R})$.

Why is $G$ Fuchsian of finite volume?

That is, why is $G$ a discrete subgroup of finite volume?

  • 0
    How do you know it is?2011-11-04
  • 0
    *How* do you view $G$ as a subgroup of $\mathrm{SL}_2(\mathbb R)$? $G$ is a finitely generated free group, and there are *many* free subgroups inside $\mathrm{SL}_2(\mathbb R)$...2011-11-04

1 Answers 1