# Dehn functions of mapping tori of right-angled Artin groups

## TL;DR

This paper classifies the Dehn functions of algebraic mapping tori of certain right-angled Artin groups based on their automorphisms, revealing how these functions depend on the automorphism structure.

## Contribution

It provides a complete classification of Dehn functions for mapping tori of specific right-angled Artin groups, including all 3-generator cases and products of free groups.

## Key findings

- Dehn functions depend on the automorphism ta; classification achieved for key classes of right-angled Artin groups.
- Explicit descriptions of Dehn functions for all 3-generator right-angled Artin groups.
- Results extend understanding of geometric properties of automorphism-induced group extensions.

## Abstract

The algebraic mapping torus $M_{\Phi}$ of a group $G$ with an automorphism $\Phi$ is the HNN-extension of $G$ in which conjugation by the stable letter performs $\Phi$. We classify the Dehn functions of $M_{\Phi}$ in terms of $\Phi$ for a number of right-angled Artin groups $G$, including all $3$-generator right-angled Artin groups and $F_k \times F_l$ for all $k,l \geq 2$.