Journal article

Universal bounds for hyperbolic Dehn surgery

CD Hodgson, SP Kerckhoff

ANNALS OF MATHEMATICS | ANNALS MATHEMATICS, FINE HALL | Published : 2005

Abstract

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.

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