On Limit Sets of 4-dimensional Kleinian Groups with 3 Generators

Abstract

In this paper, we consider a quaternionic representation of a 4-dimensional Kleinian group $G$ with 3 generators $f,g$ and $h$, where $g$ and $h$ are simple parabolic, $[g,h]= id$, and $[f,g],[f,h]$ are order-2 elliptic elements. We parameterize such $f,g$ and $h$ up to conjugacy and we simulate the shape of the limit set $\Lambda(G)$ using computer.