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.
Cite this article
Piotr Przytycki, Jacek Świątkowski, Flag-no-square triangulations and Gromov boundaries in dimension 3. Groups Geom. Dyn. 3 (2009), no. 3, pp. 453–468DOI 10.4171/GGD/66