Computing arithmetic Kleinian groups

TL;DR

This paper introduces an algorithm that computes fundamental domains and finite presentations for arithmetic Kleinian groups, enabling better understanding and manipulation of these complex mathematical structures.

Contribution

The paper presents the first algorithm to explicitly compute fundamental domains and presentations for arithmetic Kleinian groups.

Findings

Algorithm successfully computes fundamental domains.

Finite presentations are obtained with a proven isomorphism.

Enhances computational tools for Kleinian groups.

Abstract

Arithmetic Kleinian groups are arithmetic lattices in PSL_2(C). We present an algorithm which, given such a group Gamma, returns a fundamental domain and a finite presentation for Gamma with a computable isomorphism.