Hyperbolic Dehn surgery on geometrically infinite 3-manifolds

TL;DR

This paper extends Thurston's hyperbolic Dehn surgery theorem to geometrically infinite 3-manifolds and proves a density theorem for Kleinian groups, also discussing hyperbolic Dehn surgery on cone-manifolds.

Contribution

It generalizes hyperbolic Dehn surgery to a broader class of 3-manifolds and establishes a density theorem for Kleinian groups.

Findings

Extended Thurston's theorem to geometrically infinite manifolds

Proved a density theorem for Kleinian groups

Discussed hyperbolic Dehn surgery on cone-manifolds

Abstract

In this paper we extend Thurston's hyperbolic Dehn surgery theorem to a class of geometrically infinite hyperbolic 3-manifolds. As an application we prove a modest density theorem for Kleinian groups. We also discuss hyperbolic Dehn surgery on geometrically finite hypebolic cone-manifolds.