Universal bounds for hyperbolic Dehn surgery

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 cone-manifold structures, using infinitesimal harmonic deformations and analysis of geometric limits.

Authors

Craig Hodgson

Department of Mathematics and Statistics
University of Melbourne
Victoria 3010
Australia

Steven P. Kerckhoff

Department of Mathematics
Stanford University
Stanford, CA 94305
United States