A non-residually finite group acting uniformly properly on a hyperbolic space

TL;DR

This paper constructs an example of a non-residually finite group that can act in a uniformly proper way on a Gromov hyperbolic space, providing new insights into group actions on hyperbolic spaces.

Contribution

It introduces the first known example of a non-residually finite group with a uniformly proper hyperbolic space action.

Findings

Demonstrates existence of non-residually finite groups acting properly on hyperbolic spaces

Expands understanding of group actions in geometric group theory

Provides a new example challenging previous assumptions

Abstract

In this article we produce an example of a non-residually finite group which admits a uniformly proper action on a Gromov hyperbolic space.