Kleinian groups via strict hyperbolization

TL;DR

This paper constructs specific Kleinian groups using strict hyperbolization techniques from free groups, describes their limit sets, and discusses potential generalizations to other right-angled Artin groups.

Contribution

It introduces a novel method to construct Kleinian groups from free groups via strict hyperbolization and analyzes their limit sets.

Findings

Construction of Kleinian groups from free groups using hyperbolization

Description of the limit set and its topological dimension

Potential generalizations to other right-angled Artin groups

Abstract

In this paper, we construct Kleinian groups $\Gamma<\mathrm{Isom}(\mathbb{H}^{2n})$ from the direct product of $n$ copies of the rank 2 free group $F_2$ via strict hyperbolization. We give a description of the limit set and its topological dimension. Such construction can be generalized to other right-angled Artin groups.