Characterizing slopes for the $(-2,3,7)$-pretzel knot

Abstract

In this note we exhibit concrete examples of characterizing slopes for the knot $12n242$, aka the $(-2,3,7)$-pretzel knot. Although it was shown by Lackenby that every knot admits infinitely many characterizing slopes, the non-constructive nature of the proof means that there are very few hyperbolic knots for which explicit examples of characterizing slopes are known.