Every right-angled Artin group is commensurable to a right-angled Coxeter group [Davis-Januszkiewicz 2000]. In the other direction, there are some quasiisometry invariants like quadratic divergence and having totally disconnected Morse boundary that are necessary for a group to be quasiisometric to a RAAG, but these do not tell the full story. We focus on the 2--dimensional case and give conditions on the presentation graph of a RACG that imply it is quasiisometric to a RAAG and other conditions that imply it is not. Our methods completely answer the question of whether or not the RACG is quasiisometric to some RAAG when the presentation graph has at most 10 vertices.
This is joint work with Pallavi Dani, Alexandra Edletzberger, and Annette Karrer.
