On Thin Heckoid and Generalised Triangle Groups in $PSL(2,\mathbb{C})$}

TL;DR

This paper lists all 55 thin generalized triangle groups of slope 1/2 in PSL(2,C), contributing to the classification of thin Heckoid groups and their properties in complex hyperbolic geometry.

Contribution

It provides a complete enumeration of thin generalized triangle groups of slope 1/2 in PSL(2,C), advancing understanding of thin groups in complex hyperbolic geometry.

Findings

Complete list of 55 thin generalized triangle groups of slope 1/2.

Application of computational methods to classify thin groups.

Connection to the broader classification of thin Heckoid groups.

Abstract

We provide a brief overview of our upcoming work identifying all the thin Heckoid groups in $PSL(2,\mathbb{C})$. Here we give a complete list of the $55$ thin generalised triangle groups of slope $1/2$. This work was presented at the conference Computational Aspects of Thin Groups, IMSS, Singapore and presents an application of joint work initiated with Colin Maclachlan