Triangulations of the 3-sphere with knotted edge
Geometric Topology
2024-12-02 v1
Abstract
We prove that for any knot , there exists a one-vertex triangulation of the -sphere containing an edge forming . The proof is constructive, and based on fully augmented links. We use our method to produce ``complicated'' simplicial triangulations of the -sphere that we show are smallest possible, up to a constant multiplicative factor.
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