Triangulations of the 3-sphere with knotted edge
arXiv:2411.18938
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.
19 pages, 13 figures