$\mathbb{C}$-Fuchsian subgroups of some non-arithmetic lattices

TL;DR

This paper presents a method to analyze specific complex Fuchsian subgroups within non-arithmetic lattices, demonstrating that their fundamental domains are contained in a complex geodesic, akin to a unit disk.

Contribution

It introduces a general procedure for studying the structure of certain complex Fuchsian subgroups in non-arithmetic lattices and shows their fundamental domains are contained in a complex geodesic.

Findings

Fundamental domains lie in a complex geodesic.

Provides a general analysis method for these subgroups.

Shows the geometric nature of the fundamental domains.

Abstract

We give a general procedure to analyze the structure for certain $\mathbb{C}$-Fuchsian subgroups of some non-arithmetic lattices. We will also show that their fundamental domains lie in a complex geodesic, a set homeomorphic to the unit disk.