Algorithmic construction and recognition of hyperbolic 3-manifolds, links, and graphs

Abstract

This survey article describes the algorithmic approaches successfully used over the time to construct hyperbolic structures on various 3-dimensional topological “objects” (cusped manifolds, manifolds with boundary, links, graphs, orbifolds). It also exposes the classification techniques based on hyperbolic geometry and the experimental classification results of several classes of 3-dimensional topological “objects” obtained over the time.