An algorithm for finding minimal volume hyperbolic links and the Dehn parental test

Misha Schmalian

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arXiv · 2503.05671

An algorithm for finding minimal volume hyperbolic links and the Dehn parental test

Misha Schmalian

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Abstract

We describe an algorithm that, given a 3-manifold M, outputs a finite set containing all minimal volume k-component hyperbolic link complements in M. A key step, that might be of independent interest, is an algorithm that, given two 3-manifolds N and M, decides whether they are related by Dehn filling. In fact, we show that the set of boundary slopes giving a Dehn filling of N to M is determined by a special class of well-studied quadratic Diophantine (in)equalities, for which solvability is known to be decidable.

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Misha Schmalian. 2025-03-07. An algorithm for finding minimal volume hyperbolic links and the Dehn parental test. https://arxiv.org/abs/2503.05671

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