# Some groups with planar boundaries

## TL;DR

This paper explores the boundaries of hyperbolic groups through specific amalgams, illustrating key phenomena and conjectures with insights from foundational results and special cases like free groups.

## Contribution

It provides an expository overview of boundary phenomena in hyperbolic groups, highlighting special cases and fundamental results from notable researchers.

## Key findings

- Illustrates phenomena and conjectures about hyperbolic group boundaries
- Describes fundamental results by Bowditch and Haissinsky
- Examines boundaries of free groups with special treatments

## Abstract

In this expository note, we illustrate phenomena and conjectures about boundaries of hyperbolic groups by considering the special cases of certain amalgams of hyperbolic groups. While doing so, we describe fundamental results on hyperbolic groups and their boundaries by Bowditch and Haissinsky, along with special treatments for the boundaries of free groups by Otal and Cashen.