Vertex distortion detects the unknot
Geometric Topology
2022-12-21 v2
Abstract
The first two authors introduced vertex distortion and showed that the vertex distortion of the unknot is trivial. It was conjectured that the vertex distortion of a knot is trivial if and only if the knot is trivial. We will use Denne-Sullivan's bound on Gromov distortion to bound the vertex distortion of nontrivial lattice knots. We will then conclude that trivial vertex distortion implies the unknot, proving the conjecture. Additionally, the first conjecture in vertex distortion's debut article is proven and a vertex distortion calculator is given.
Keywords
Cite
@article{arxiv.2110.14119,
title = {Vertex distortion detects the unknot},
author = {Marion Campisi and Nicholas Cazet and David Crncevic and Tasha Fellman and Phillip Kessler and Nikolas Rieke and Vatsal Srivastava and Luis Torres},
journal= {arXiv preprint arXiv:2110.14119},
year = {2022}
}
Comments
12 pages, 6 figures