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Modifications preserving hyperbolicity of link complements

Colin Adams, William H Meeks III and Álvaro K Ramos

Algebraic & Geometric Topology 23 (2023) 2157–2190
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.

Keywords
hyperbolic 3–manifold, hyperbolic link complement, chain move, switch move
Mathematical Subject Classification
Primary: 57K10, 57K32
References
Publication
Received: 30 December 2020
Revised: 3 February 2022
Accepted: 9 March 2022
Published: 25 July 2023
Authors
Colin Adams
Department of Mathematics
Williams College
Williamstown, MA
United States
William H Meeks III
Department of Mathematics and Statistics
University of Massachusetts
Amherst, MA
United States
Álvaro K Ramos
Departamento de Matemática Pura e Aplicada
Universidade Federal do Rio Grande do Sul
Porto Alegre
Brazil

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