Displaying similar documents to “Hyperbolic 4-manifolds and tesselations”

Geometric orbifolds.

William D. Dunbar (1988)

Revista Matemática de la Universidad Complutense de Madrid


An orbifold is a topological space which ?locally looks like? the orbit space of a properly discontinuous group action on a manifold. After a brief review of basic concepts, we consider the special case 3-dimensional orbifolds of the form GammaM, where M is a simply-connected 3-dimensional homogeneous space corresponding to one of Thurston?s eight geometries, and where Gamma < Isom(M) acts properly discontinuously. A general description of these geometric orbifolds is given and...

Some examples of essential laminations in 3-manifolds

Allen Hatcher (1992)

Annales de l'institut Fourier


Families of codimension-one foliations and laminations are constructed in certain 3-manifolds, with the property that their transverse intersection with the boundary torus of the manifold consists of parallel curves whose slope varies continuously with certain parameters in the construction. The 3-manifolds are 2-bridge knot complements and punctured-torus bundles.

Polyhedral realisation of hyperbolic metrics with conical singularities on compact surfaces

François Fillastre (2007)

Annales de l’institut Fourier


A Fuchsian polyhedron in hyperbolic space is a polyhedral surface invariant under the action of a Fuchsian group of isometries (i.e. a group of isometries leaving globally invariant a totally geodesic surface, on which it acts cocompactly). The induced metric on a convex Fuchsian polyhedron is isometric to a hyperbolic metric with conical singularities of positive singular curvature on a compact surface of genus greater than one. We prove that these metrics are actually realised by exactly...

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.

Dehn filling: A survey

C. Gordon (1998)

Banach Center Publications


In this paper we give a brief survey of the present state of knowledge on exceptional Dehn fillings on 3-manifolds with torus boundary. For our discussion, it is necessary to first give a quick overview of what is presently known, and what is conjectured, about the structure of 3-manifolds. This is done in Section 2. In Section 3 we summarize the known bounds on the distances between various kinds of exceptional Dehn fillings, and compare these with the distances that arise in known...