# Vertex of Fundamental Domains & Elliptic Points

1. Apr 25, 2012

### Fangyang Tian

Dear Folks:
Suppose $\Gamma$ is a discrete subgroup of SL2(R), which acts on the upper half complex plane as Mobius transformation. F is its fundamental domain. If z is a vertex of F which does not lie on the extended real line ( that is R$\bigcup$$\infty$ ) ,then must x be an elliptic point?? Many thanks!!
For example, if $\Gamma$ is SL2(Z), then x is either ei$\frac{2}{3}$$\pi$ or ei$\frac{4}{3}$$\pi$, both of them are elliptic points.