A Note on Hyperbolically Embedded Subgroups

TL;DR

This paper presents an alternative definition of hyperbolically embedded subgroups using Bowditch's framework, aiming to clarify their structure within relatively hyperbolic groups through fine graphs.

Contribution

It introduces an equivalent, more accessible definition of hyperbolically embedded subgroups based on Bowditch's approach, enhancing understanding of their properties.

Findings

Provides an equivalent definition of hyperbolically embedded subgroups.

Connects hyperbolic embedding with Bowditch's approach to relative hyperbolicity.

Facilitates analysis of subgroup structures in relatively hyperbolic groups.

Abstract

Let $G$ be a group and $H$ a subgroup of $G$. This note introduces an equivalent definition of hyperbolic embedded subgroup based on Bowditch's approach to relatively hyperbolic groups in terms of fine graphs.