# Subgroup distortion of 3-manifold groups

## TL;DR

This paper classifies the possible subgroup distortions in finitely generated 3-manifold groups, revealing they are limited to linear, quadratic, exponential, or double exponential, and links distortion to subgroup separability.

## Contribution

It provides a complete computation of subgroup distortion types in all finitely generated 3-manifold groups and establishes their relation to subgroup separability.

## Key findings

- Subgroup distortion in 3-manifold groups is only linear, quadratic, exponential, or double exponential.
- Distortion type is closely related to the subgroup's separability.
- The work offers a comprehensive classification of subgroup distortion in this class of groups.

## Abstract

In this paper, we compute the subgroup distortion of all finitely generated subgroups of all finitely generated 3-manifold groups, and the subgroup distortion in this case can only be linear, quadratic, exponential and double exponential. It turns out that the subgroup distortion of a subgroup of a 3-manifold group is closely related to the separability of this subgroup.