Dehn functions of mapping tori of right-angled Artin groups (Q6634400)

Algebraic mapping tori are fundamental groups of topological mapping tori of surfaces or complexes. For a finitely presented group \(G =\langle X \mid R \rangle\) and an injective endomorphism \(\Phi : G \rightarrow G\), the algebraic mapping torus is the group \(M_{\Phi}=\langle X, t \mid R, t^{-1}xt= \Phi(x), \; \forall x \in X \rangle\). In the paper under review the authors consider the case where \(\Phi\) is an automorphism (so \(M_{\Phi} = G \rtimes_{\Phi} \mathbb{Z}\)), and \(G\) is a right-angled Artin group (\(\mathsf{RAAGs}\)-groups). They classify the Dehn functions of \(M_{\Phi}\) in terms of \(\Phi\) for a number of \(\mathsf{RAAGs}\)-groups \(G\), including all 3-generator \(\mathsf{RAAGs}\)-groups and \(F_{k} \times F_{\ell}\) for all \(k, \ell \geq 2\) (here \(F_{n}\) denotes the free group of rank \(n\)).