Subroups of $PSL(3,\Bbb{C})$ with four lines in general position in its Limit Set

TL;DR

This paper characterizes subgroups of PSL(3,C) whose limit set consists of four lines in general position, and shows the equicontinuity set coincides with the discontinuity set for these groups.

Contribution

It provides an algebraic characterization of PSL(3,C) subgroups with four-line limit sets and analyzes their discontinuity and equicontinuity sets.

Findings

Limit set consists of four lines in general position.

Equicontinuity set equals the discontinuity set for these groups.

Provides algebraic criteria for such groups.

Abstract

In this article we provide an algebraic characterization of those groups of $PSL(3,\Bbb{C})$ whose limit set in the Kulkarni sense has, exactly, four lines in general position. Also we show that, for this class of groups, the equicontinuity set of the group is the largest open set where the group acts discontinuously and agrees with the discontinuity set of the group.