Dehn functions of mapping tori of right-angled Artin groups

Abstract

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 (RAAGs) $G$ , including all $3$ -generator RAAGs and $F_k \times F_l$ for all $k,l \geq 2$ .