### Hyperbolic 4-manifolds and conformally flat 3-manifolds

Michael Gromov, H. B. Jr. Lawson, W. Thurston (1988)

Publications Mathématiques de l'IHÉS

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Michael Gromov, H. B. Jr. Lawson, W. Thurston (1988)

Publications Mathématiques de l'IHÉS

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William D. Dunbar (1988)

Revista Matemática de la Universidad Complutense de Madrid

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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...

Masters, Joseph D. (2005)

Algebraic & Geometric Topology

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Ivanšić, Dubravko, Ratcliffe, John G., Tschantz, Steven T. (2005)

Algebraic & Geometric Topology

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Bachman, David, Cooper, Daryl, White, Matthew E. (2004)

Algebraic & Geometric Topology

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Allen Hatcher (1992)

Annales de l'institut Fourier

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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.

François Fillastre (2007)

Annales de l’institut Fourier

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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...

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.

Brinkmann, Peter, Schleimer, Saul (2001)

Experimental Mathematics

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C. Gordon (1998)

Banach Center Publications

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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...