# Hyperfiniteness of boundary actions of hyperbolic groups

## TL;DR

This paper proves that the boundary action of any finitely generated hyperbolic group results in a hyperfinite equivalence relation, advancing understanding of the group's boundary dynamics.

## Contribution

It establishes the hyperfiniteness of boundary actions for all finitely generated hyperbolic groups, a novel result in geometric group theory.

## Key findings

- Boundary actions induce hyperfinite equivalence relations
- Applicable to all finitely generated hyperbolic groups
- Enhances understanding of boundary dynamics in hyperbolic groups

## Abstract

We prove that for every finitely generated hyperbolic group $G$, the action of $G$ on its Gromov boundary induces a hyperfinite equivalence relation.