Three-dimensional orbifolds and cone-manifolds

By Daryl Cooper, Craig Hodgson, S. Kerckhoff. 2000

269 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/72f992ec611f2cbd9569d5f13706dce7c66eff2f

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

In Geometry and Topology

Citations in the corpus

Three-Dimensional Orbifolds and Their Geometric Structures (2003, background): “Recently in 2000, two different proofs were worked out, see [16, 17] and [43].”
Real hyperbolic on the outside, complex hyperbolic on the inside (2003, methodology): “5. Once we analyze the topology of Ω(4, 7)/∆(4, 7), it might be possible to show that the orbifold is hyperbolic by combining results in [FH] with Thurston’s Orbifold Theorem [BLP], [ CHK ].”
Geometrization of Three-Dimensional Orbifolds via Ricci Flow (2011, background): “In the early 1980’s Thurston announced a proof of the conjecture for Haken manifolds [57], with written proofs appearing much later [34, 39, 45, 46].”
Generalizations of McShane's identity to hyperbolic cone-surfaces (2004, background): “orkers, see [2], [22]. In this paper we further generalize McShane’s identity as in Theorem 1.2 to the cases of hyperbolic cone-surfaces possibly with cusps and/or geodesic boundary. (See for example [10] for basic facts on cone-manifolds.) We assume that all cone points have cone angle ≤ π (except ”
Epimorphisms between 2-bridge link groups (2009, methodology): “By the classification of exceptional surgeries on hyperbolic 2-bridge knots due to Brittenham-Wu [7] and by the orbifold theorem [2, 9], we can choose Ki so that every Mi is hyperbolic.”
Tameness of hyperbolic 3-manifolds (2004, methodology): “One may also prove this using the orbifold theorem [7, 24]).”
Geometrization of 3-dimensional orbifolds (2000, unknown): “A different proof was announced in [CHK].”
Dehn filling, volume, and the Jones polynomial (2006, methodology): “. Theorem 1.1 also leads to lower bounds on the volumes of Dehn ﬁllings of link complements in S3 and branched coverings of S3 over links. For example, combining Theorem 1.1 with the orbifold theorem [10, 16] and a result of Adams on the waist size of knots [4] yields the following result. Theorem 1”
3-Manifold Groups (2012, background): “A detailed sketch of the proof appears in [CHK00], and full details of the proof appear in [BP01, BLP01, BLP05] and [BMP03, Theorem 3.”