Knots not detected by any trace

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.

8 pages, 6 figures; V2: Minor changes, version accepted for publication in Int. Math. Res. Not. IMRN