Andreev’s Theorem on 3-dimensional Hyperbolic Polyhedra

Abstract:

Andreev’s Theorem (1970) gives us a classification of polyhedra of finite volume, with non-obtuse dihedral angles, in the 3-dimensional hyperbolic space. The main pur- pose of this thesis is to give an introduction to such polyhedra and their combinatorics, and to study the tools used by Andreev to state and prove his theorem.