Triangulations of the 3-sphere with knotted edge

Journal of Combinatorial Theory Series A 2026 Open access

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Authors: Dionne Ibarra, Daniel V. Mathews, Jessica S. Purcell, Jonathan Spreer
DOI: 10.1016/j.jcta.2026.106269
Cited by: 0
References: 39

Abstract

We prove that for any knot K , there exists a decomposition of the 3-sphere into tetrahedra such that a representative of K is formed from one vertex and one edge of the decomposition. The proof is constructive, and based on fully augmented links. We use our method to produce a family of simplicial triangulations of the 3-sphere with a loop of four edges representing a t -fold connected sum of the trefoil, whose number of tetrahedra grows linearly in t . This is best possible up to a constant factor.

Fields of Study & Subjects

Computational Geometry and Mesh Generation Advanced Numerical Analysis Techniques Digital Image Processing Techniques

Publication details

Journal / source
Journal of Combinatorial Theory Series A
Publisher
Elsevier BV
Volume
226
Pages
106269–106269
Publication date
18 September 2026
Language
EN