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Displaying similar documents to “Systolic groups acting on complexes with no flats are word-hyperbolic”

Boundaries of right-angled hyperbolic buildings

Jan Dymara, Damian Osajda (2007)

Fundamenta Mathematicae

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We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. As a consequence, the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.

Some generalized Coxeter groups and their orbifolds.

Marcel Hagelberg, Rubén A. Hidalgo (1997)

Revista Matemática Iberoamericana

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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.

Some Connections between Minkowski and Hyperbolic Planes

Jarosław Kosiorek, Andrzej Matraś (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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The model of the Minkowski plane in the projective plane with a fixed conic sheds a new light on the connection between the Minkowski and hyperbolic geometries. The construction of the Minkowski plane in a hyperbolic plane over a Euclidean field is given. It is also proved that the geometry in an orthogonal bundle of circles is hyperbolic in a natural way.