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Universal bounds for hyperbolic Dehn surgery

Craig D. Hodgson·Steven P. Kerckhoff
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Abstract

This paper gives a quantitative version of Thurston's hyperbolic Dehn surgery theorem. Applications include the first universal bounds on the number of non-hyperbolic 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 cone-manifold structures, using infinitesimal harmonic deformations and analysis of geometric limits.

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Craig D. Hodgson, Steven P. Kerckhoff. 2002-04-30. Universal bounds for hyperbolic Dehn surgery. https://arxiv.org/abs/math/0204345

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