Fully augmented links in the thickened torus

Kwon, Alice

doi:10.2140/agt.2025.25.1411

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Fully augmented links in the thickened torus

Alice Kwon

Algebraic & Geometric Topology 25 (2025) 1411–1432

DOI: 10.2140/agt.2025.25.1411

Abstract

We study the geometry of fully augmented link complements in the thickened torus and describe their geometric properties, generalizing the study of fully augmented links in $S^{3}$ . We classify which fully augmented links in the thickened torus are hyperbolic, and show that their complements in the thickened torus decompose into ideal right-angled torihedra. We also study volume density of fully augmented links in $S^{3}$ , defined to be the ratio of its volume and the number of augmentations. We prove the volume density conjecture for fully augmented links, which states that the volume density of a sequence of fully augmented links in $S^{3}$ which diagrammatically converges to a biperiodic link converges to the volume density of that biperiodic link. Furthermore, we show that the complement of a sequence of these links approaches the complement of the biperiodic link as a geometric limit.

Keywords

geometric topology, fully augmented links

Mathematical Subject Classification

Primary: 57K10, 57K32, 57M50

References

Publication

Received: 19 August 2022

Revised: 22 May 2023

Accepted: 13 August 2023

Published: 20 June 2025

Authors

Alice Kwon
Science Department SUNY Maritime Throggs Neck, NY United States

Work by the US Government, under license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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Volume 25, issue 3 (2025)