Flag-no-square triangulations and Gromov boundaries in dimension 3

Abstract

We describe an infinite family of 3-dimensional topological spaces, which are homeomorphic to boundaries of certain word-hyperbolic groups. The groups are right-angled hyperbolic Coxeter groups, whose nerves are flag-no-square triangulations of 3-dimensional manifolds. We prove that any 3-dimensional polyhedral complex (in particular, any 3-manifold) can be triangulated in a flag-no-square way.