Modifications preserving hyperbolicity of link complements

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.