I started reading about Hyperbolic manifolds here: https://en.m.wikipedia.org/wiki/Hyperbolic_manifold and I didn't understand the following paragraph in the first section of Rigourous definition:
Every complete, connected, simply-connected manifold of constant negative curvature -1 is isometric to a real Hyperbolic space $\mathbb{H}^n.$ Thus, every such $M$ can be written as $\mathbb{H}^n/ \Gamma$ where $\Gamma$ is a torsion free discrete group of isometries on $\mathbb{H}^n.$
Could anyone explain to me why does every such $M$ can be written as $\mathbb{H}^n/ \Gamma$ where $\Gamma$ is a torsion free discrete group of isometries on $\mathbb{H}^n$ ?