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

TL;DR

This survey reviews algorithmic methods for constructing and classifying hyperbolic structures on 3-dimensional topological objects, including manifolds, links, and graphs, highlighting progress and techniques in the field.

Contribution

It compiles and discusses various algorithmic approaches for constructing and recognizing hyperbolic 3-manifolds, providing a comprehensive overview of the field.

Findings

Successful algorithms for hyperbolic structure construction

Classification methods for hyperbolic 3-manifolds

Application to links and graphs

Abstract

This survey article describes the algorithmic approaches successfully used over the time to construct hyperbolic structures on 3-dimensional topological "objects" of various types, and to classify several classes of such objects using such structures.