A **Fuchsian group** is a discrete subgroup of $\mathrm{PSL}(2,\mathbb{R})$ for the natural topology induced by the topology of $2\times
2$ real matrices.

We say that a Fuchsian group is of
the **first kind** if it has finite covolume for the hyperbolic metric $d\mu=dxdy/y^2$, i.e.
\[
\text{covol}(G)=\int_{\mathfrak{F}(G)}d\mu<\infty,
\]
where $\mathfrak{F}(G)$ is the fundamental domain of $G$.

**Authors:**

**Knowl status:**

- Review status: beta
- Last edited by Jennifer Paulhus on 2020-07-16 18:25:36

**Referred to by:**

**History:**(expand/hide all)

**Differences**(show/hide)