# (Un)distorted stabilisers in the handlebody group

## TL;DR

This paper investigates the geometric distortion properties of stabilisers in the handlebody group, revealing that some are undistorted while others exhibit exponential distortion depending on the type of stabiliser and genus.

## Contribution

It provides a detailed analysis of the distortion properties of various stabilisers in the handlebody group, highlighting differences based on stabiliser type and genus.

## Key findings

- Stabilisers of meridians are undistorted.
- Stabilisers of primitive curves or annuli are exponentially distorted.
- Distortion depends on the genus of the handlebody.

## Abstract

We study geometric properties of stabilisers in the handlebody group. We find that stabilisers of meridians are undistorted, while stabilisers of primitive curves or annuli are exponentially distorted for large enough genus.