Modifications Preserving Hyperbolicity of Link Complements

TL;DR

This paper introduces two modifications, the chain move and switch move, that preserve hyperbolicity of link complements in 3-manifolds, significantly expanding the catalog of known hyperbolic links.

Contribution

It presents new modifications that preserve hyperbolicity and classifies the exceptions, enhancing understanding of hyperbolic link complements.

Findings

Two modifications preserve hyperbolicity in most cases.

Classified a small set of exceptions.

Increased known hyperbolic links in 3-sphere and other manifolds.

Abstract

Given a link in a 3-manifold such that the complement is hyperbolic, we provide two modifications to the link, called the chain move and the switch move, that preserve hyperbolicity of the complement, with only a relatively small number of manifold-link pair exceptions, which are also classified. These modifications provide a substantial increase in the number of known hyperbolic links in the 3-sphere and other 3-manifolds.