Universal bounds for hyperbolic Dehn surgery

By Craig Hodgson, S. Kerckhoff. 2002

126 citations recorded by the source corpus.

This paper gives a quantitative version of Thurston?s hyperbolic Dehn surgery theorem. Applications include the first universal bounds on the number of nonhyperbolic Dehn fillings on a cusped hyperbolic 3-manifold, and estimates on the changes in volume and core geodesic length during hyperbolic Dehn filling. The proofs involve the construction of a family of hyperbolic conemanifold structures, using infinitesimal harmonic deformations and analysis of geometric limits.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1138a175a1ad64d23410f3cc2e3d13074b25d85b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Links with no exceptional surgeries (2004, background): “Crowell [4] and Murasugi [15] have independently proved that the genus of an alternating link is equal to half the degree of its Alexander polynomial, and Gabai [7] gave an algorithm to compute the genus of an arborescent link.”
The maximal number of exceptional Dehn surgeries (2008, background): “A third approach, due to Hodgson and Kerckhoff [19], aims to prove that M(s) is hyperbolic without appealing to the geometrisation conjecture.”
On the density of geometrically finite Kleinian groups (2002, background): “The theory of deformations of these manifolds that change only the cone-angle, developed by C. Hodgson, S. Kerckho [HK1, HK2 , HK4] and the second author [Brm1, Brm2], is instrumental in our study.”
Twisted cohomology for hyperbolic three manifolds (2010, unknown): “More precisely, we require that there is a continuous path of cone manifold structures with cone angle (cid:11) 2 [0, 2 (cid:25) ], so that (cid:11) 0 is the complete structure on M and (cid:11) 2 (cid:25) is the ﬁlled manifold (cf. [26, 17]).”
Cannon-Thurston Maps for Surface Groups (2006, methodology): “mly bi-Lipschitz. This allows us to pass back and forth between the drilled and ’undrilled’ manifolds. The Drilling Theorem of Brock and Bromberg [6], which built on work of Hodgson and Kerckhoﬀ [20] [21] is given below. We shall invoke a version of this theorem which is closely related to one used ”
Three-Dimensional Orbifolds and Their Geometric Structures (2003, background): “Kerckhoff [111] obtained a universal bound on the number of exceptional slopes for Dehn fillings on an orientable finite volume hyperbolic 3-manifold with one cusp.”
Dehn filling in relatively hyperbolic groups (2006, background): “Since we are, from the very beginning, working in the coarse world of δ-hyperbolic spaces, we have no hope of obtaining the fine control over constants, as obtained in [20, 1, 18].”
Positively oriented ideal triangulations on hyperbolic three-manifolds (2004, background): “Moreover, they have shown that for a hyperbolic cone-manifold, if there exists a tube of radius R¿ arcsinh 1= √ 2 around the singular locus then the length of the singular locus increases with the cone-angle [6].”