Knots not detected by any trace

Kenneth L. Baker; Marc Kegel; Kimihiko Motegi

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arXiv · 2503.14172

Knots not detected by any trace

Kenneth L. Baker·Marc Kegel·Kimihiko Motegi

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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.

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BibTeX RIS

Kenneth L. Baker, Marc Kegel, Kimihiko Motegi. 2025-03-18. Knots not detected by any trace. https://arxiv.org/abs/2503.14172

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