Kleinian Groups with a Control Group

Abstract

Nowadays the literature and the knowledge about subgroups of PSL(2, $\mathbb{C}$) is vast. Thence, when going up into higher dimensions, a natural step is to consider Kleinian subgroups of PSL(3, $\mathbb{C}$) whose geometry and dynamics are “governed” by a subgroup of PSL(2, $\mathbb{C}$). That is the subject we address in this chapter. The corresponding subgroup in PSL(2 ,$\mathbb{C}$) is the control group. These groups play a significant role in the classification theorems we give in Chapter 8.