Nielsen equivalence in triangle groups

TL;DR

This paper extends previous work to show that any generating pair of a triangle group can be represented by a special almost orbifold covering, deepening understanding of the structure of triangle groups.

Contribution

It generalizes the result of Dutra to all generating pairs of triangle groups, providing a new geometric representation method.

Findings

Any generating pair of a triangle group is represented by a special almost orbifold covering.

The result broadens the understanding of the structure of triangle groups.

Provides a geometric perspective on generating pairs in triangle groups.

Abstract

We extend the result of \cite{Dutra} to generating pairs of triangle groups, that is, we show that any generating pair of a triangle group is represented by a special almost orbifold covering.