A finitely presented subgroup of the automorphism group of a right-angled Artin group

TL;DR

This paper computes a finite presentation for a subgroup of automorphisms of a right-angled Artin group that send generators to conjugates, extending McCool's work on free groups using geometric methods.

Contribution

It provides a new finite presentation for a specific automorphism subgroup of right-angled Artin groups, generalizing previous results for free groups.

Findings

Computed a finite presentation for the subgroup H of Aut(G)

Extended McCool's results from free groups to right-angled Artin groups

Used geometric methods to achieve the presentation

Abstract

Let G be a right-angled Artin group. We use geometric methods to compute a presentation of the subgroup H of Aut(G) consisting of the automorphisms that send each generator to a conjugate of itself. This generalizes a result of McCool on basis-conjugating automorphisms of free groups.