Triangulations of the 3-sphere with knotted edge

Dionne Ibarra; Daniel V. Mathews; Jessica S. Purcell; Jonathan Spreer

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arXiv · 2411.18938

Triangulations of the 3-sphere with knotted edge

Dionne Ibarra·Daniel V. Mathews·Jessica S. Purcell·Jonathan Spreer

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Abstract

We prove that for any knot $K$, there exists a one-vertex triangulation of the $3$-sphere containing an edge forming $K$. The proof is constructive, and based on fully augmented links. We use our method to produce ``complicated'' simplicial triangulations of the $3$-sphere that we show are smallest possible, up to a constant multiplicative factor.

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BibTeX RIS

Dionne Ibarra, Daniel V. Mathews, Jessica S. Purcell, Jonathan Spreer. 2024-11-28. Triangulations of the 3-sphere with knotted edge. https://arxiv.org/abs/2411.18938

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