Journal of Combinatorial Theory Series A· 2026Q1
Triangulations of the 3-sphere with knotted edge
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- Q1SCImago
- 2026year
Short summary
Any knot K can be represented by a single vertex and edge within a tetrahedral decomposition of the 3-sphere.
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Key points
- Any knot K can be represented by a single vertex and edge in a 3-sphere's tetrahedral decomposition.
- The proof is constructive and relies on fully augmented links.
- A family of triangulations for connected sums of the trefoil knot is produced.
- The number of tetrahedra in these triangulations grows linearly with the connected sum order (t), which is optimal.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Journal of Combinatorial Theory Series A, 2026 · DOI ↗
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Field: Computer Graphics and Computer-Aided Design
Computer Graphics and Computer-Aided DesignComputer Science