English

Triangulations of the 3-sphere with knotted edge

Geometric Topology 2024-12-02 v1

Abstract

We prove that for any knot KK, there exists a one-vertex triangulation of the 33-sphere containing an edge forming KK. The proof is constructive, and based on fully augmented links. We use our method to produce ``complicated'' simplicial triangulations of the 33-sphere that we show are smallest possible, up to a constant multiplicative factor.

Keywords

Cite

@article{arxiv.2411.18938,
  title  = {Triangulations of the 3-sphere with knotted edge},
  author = {Dionne Ibarra and Daniel V. Mathews and Jessica S. Purcell and Jonathan Spreer},
  journal= {arXiv preprint arXiv:2411.18938},
  year   = {2024}
}

Comments

19 pages, 13 figures