Journal article

The shape of hyperbolic Dehn surgery space

Craig D Hodgson, Steven P Kerckhoff

GEOMETRY & TOPOLOGY | GEOMETRY & TOPOLOGY PUBLICATIONS | Published : 2008

Abstract

In this paper we develop a new theory of infinitesimal harmonic deformations for compact hyperbolic 3-manifolds with "tubular boundary". In particular, this applies to complements of tubes of radius at least R0 = arctanh(1/root 3) ≈ 0.65848 around the singular set of hyperbolic cone manifolds, removing the previous restrictions on cone angles. We then apply this to obtain a new quantitative version of Thurston's hyperbolic Dehn surgery theorem, showing that all generalized Dehn surgery coefficients outside a disc of "uniform" size yield hyperbolic structures. Here the size of a surgery coefficient is measured using the Euclidean metric on a horospherical cross section to a cusp in the comple..

View full abstract

University of Melbourne Researchers