Displaying similar documents to “Coxeter groups, Salem numbers and the Hilbert metric”

Some generalized Coxeter groups and their orbifolds.

Marcel Hagelberg, Rubén A. Hidalgo (1997)

Revista Matemática Iberoamericana


In this note we construct examples of geometric 3-orbifolds with (orbifold) fundamental group isomorphic to a (Z-extension of a) generalized Coxeter group. Some of these orbifolds have either euclidean, spherical or hyperbolic structure. As an application, we obtain an alternative proof of theorem 1 of Hagelberg, Maclaughlan and Rosenberg in [5]. We also obtain a similar result for generalized Coxeter groups.

Systolic groups acting on complexes with no flats are word-hyperbolic

Piotr Przytycki (2007)

Fundamenta Mathematicae


We prove that if a group acts properly and cocompactly on a systolic complex, in whose 1-skeleton there is no isometrically embedded copy of the 1-skeleton of an equilaterally triangulated Euclidean plane, then the group is word-hyperbolic. This was conjectured by D. T. Wise.