The shape of hyperbolic Dehn surgery space

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 R 0 D arctanh.1= p 3/ 0:65848 around the singular set of hyperbolic cone manifolds, removing the previous restrictions on cone angles.