Small generators of cocompact arithmetic Fuchsian groups

TL;DR

This paper introduces a dynamical method to construct fundamental regions for cocompact arithmetic Fuchsian groups, enabling the determination of small generators for these groups.

Contribution

It provides a new dynamical approach to explicitly find small generators for cocompact arithmetic Fuchsian groups, which was previously a complex problem.

Findings

Constructed fundamental regions for these groups.

Identified small generators from the fundamental regions.

Enhanced understanding of the structure of cocompact arithmetic Fuchsian groups.

Abstract

In the study of Fuchsian groups, it is a nontrivial problem to determine a set of generators. Using a dynamical approach we construct for any cocompact arithmetic Fuchsian group a fundamental region in $\mathbf{SL}_2(\mathbb{R})$ from which we determine a set of small generators.