I am reading Silverman's book about elliptic curves.
$\Gamma(1):=SL_{2}(\mathbb{Z})/\{\pm 1\}$ is the modular group, and $H$ is the upper half plane. The author says that the geometric description of $\Gamma(1)\setminus H$ is the fundamental domain, and then he gives the picture.
I understand the fundamental domain part, but I don't understand why it is(topologically) a 2-sphere with one point missing.