Groups, Geometry, and Dynamics


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Volume 3, Issue 3, 2009, pp. 453–468
DOI: 10.4171/GGD/66

Published online: 2009-09-30

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

Piotr Przytycki[1] and Jacek Świątkowski[2]

(1) McGill University, Montreal, Canada
(2) Uniwersytet Wrocławski, Wroclaw, Poland

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.

Keywords: Word-hyperbolic group, Gromov boundary, flag-no-square triangulation

Przytycki Piotr, Świątkowski Jacek: Flag-no-square triangulations and Gromov boundaries in dimension 3. Groups Geom. Dyn. 3 (2009), 453-468. doi: 10.4171/GGD/66