Hyperbolic boundaries vs. hyperbolic groups

TL;DR

This paper explores the connections between hyperbolic and relatively hyperbolic groups and their applications to manifolds and Kleinian groups, providing a survey of key theories and examples in the field.

Contribution

It offers a comprehensive survey linking hyperbolic group theory to geometric structures like manifolds and Kleinian groups, highlighting recent developments and examples.

Findings

Survey of extensive work in hyperbolic group theory

Connections established between group theory and geometric structures

Illustrative examples of hyperbolic and Kleinian groups

Abstract

The aim of these notes is to connect the theory of hyperbolic and relatively hyperbolic groups to the theory of manifolds and Kleinian groups. We survey some of the extensive work that has been done in the field, and explain many examples. These notes are based on lectures given by the third author at CIRM in the Summer of 2018.