Polygonal $\mathcal{VH}$ Complexes

Abstract

Ian Leary inquires whether a class of hyperbolic finitely presented groups are residually finite. We answer in the affirmative by giving a systematic version of a construction in his paper, which shows that the standard $2$-complexes of these presentations have a $\mathcal{VH}$-structure. This structure induces a splitting of these groups, which together with hyperbolicity, implies that these groups are residually finite.