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Geometric triangulations and highly twisted links

Sophie L Ham and Jessica S Purcell

Algebraic & Geometric Topology 23 (2023) 1399–1462
Abstract

It is conjectured that every cusped hyperbolic 3–manifold admits a geometric triangulation, that is, it can be decomposed into positive volume ideal hyperbolic tetrahedra. We show that sufficiently highly twisted knots admit a geometric triangulation. In addition, by extending work of Guéritaud and Schleimer, we also give quantified versions of this result for infinite families of examples.

Keywords
geometric triangulation, hyperbolic knots, fully augmented link, Dehn filling
Mathematical Subject Classification
Primary: 57K10, 57K31, 57K32, 57R05
References
Publication
Received: 13 May 2021
Revised: 25 August 2021
Accepted: 19 September 2021
Published: 6 June 2023
Authors
Sophie L Ham
School of Mathematics
Monash University
Clayton
Australia
School of Mathematics and Statistics
The University of Sydney
Sydney
Australia
Jessica S Purcell
School of Mathematics
Monash University
Clayton
Australia

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