Kleinian groups in higher dimensions

TL;DR

This paper surveys higher-dimensional Kleinian groups, focusing on their topological and geometric properties and contrasting them with groups in hyperbolic 3-space, highlighting differences in structure and behavior.

Contribution

It provides a comprehensive overview of higher-dimensional Kleinian groups, emphasizing their unique topological and geometric features compared to the well-studied 3-dimensional case.

Findings

Higher-dimensional Kleinian groups exhibit distinct topological properties.

Geometric structures in higher dimensions differ significantly from those in three dimensions.

The survey highlights contrasts and similarities with hyperbolic 3-space groups.

Abstract

This is a survey of higher-dimensional Kleinian groups, i.e., discrete isometry groups of the hyperbolic n-space for n greater than 3. Our main emphasis is on the topological and geometric aspects of higher-dimensional Kleinian groups and their contrast with the discrete groups of isometry of the hyperbolic 3-space.