Practical bounds for a Dehn parental test

TL;DR

This paper develops practical bounds based on Hodgson and Kerckhoff's theorem to create an algorithm that determines if one hyperbolic 3-manifold is a Dehn filling of another, aiding in understanding hyperbolic Dehn surgery space.

Contribution

It introduces bounds and an algorithm leveraging Hodgson and Kerckhoff's theorem to effectively identify Dehn fillings among hyperbolic 3-manifolds.

Findings

Derived bounds enable practical Dehn filling detection

Algorithm can distinguish Dehn fillings of hyperbolic 3-manifolds

Utilizes Hodgson and Kerckhoff's theorem for effective computations

Abstract

In their article "The shape of hyperbolic Dehn surgery space," Hodgson and Kerckhoff proved a powerful theorem, half of which they used to make Thurston's Dehn surgery theorem effective. The calculations derived here use both halves of Hodgson and Kerckhoff's theorem to give bounds leading towards a practical algorithm to tell, given two orientable hyperbolic 3-manifolds M, N of finite volume, whether or not M is a Dehn filling of N.