Finitely presented kernels of right-angled Artin groups with abelian quotients

Abstract

In this article, we characterise when the kernels of right-angled Artin groups with abelian quotients are finitely generated and finitely presented -- exhibiting an explicit finite generating set and finite presentation. As an application, we deduce the finite presentation of the kernel of any character of a right-angled Artin group. These results generalise the presentation of the kernel of a rational character of a right-angled Artin group given by Casals--Kazachkov--Roy and Dicks and Leary's presentations of Bestina--Brady groups.