Knots not detected by any trace
Geometric Topology
2025-12-16 v2
Abstract
The first and last named authors have demonstrated the existence of knots for which every integral slope is non-characterizing. In this short note, we extend this result in two ways. There exists a knot that shares for every integer n the same n-trace with infinitely many mutually distinct knots. Moreover, every knot is concordant to a knot that is not detected by any of its traces.
Keywords
Cite
@article{arxiv.2503.14172,
title = {Knots not detected by any trace},
author = {Kenneth L. Baker and Marc Kegel and Kimihiko Motegi},
journal= {arXiv preprint arXiv:2503.14172},
year = {2025}
}
Comments
8 pages, 6 figures; V2: Minor changes, version accepted for publication in Int. Math. Res. Not. IMRN