Hyperbolic 3-manifolds

In 2003 Perelman proved Thurston's geometrization conjecture, which states that every prime closed 3-manifold can be uniquely split into components, each admitting exactly one of the eight Thurston's geometries. We will show different ways of contructing 3-manifolds (Dehn surgery, glueing poyhedra) and will argue that out of the eight possible geometries, the hyperbolic geometry is the most common one. We will also demonstrate how to visualize hyerbolic manifolds and how to perform computations on them, which we will do in real-time.