A bound on the number of twice-punctured tori in a knot exterior

Abstract

We continue a program due to Motegi regarding universal bounds for the number of non-isotopic essential n-punctured tori in the complement of a hyperbolic knot in $S^3$. For $n = 1$, Valdez-Sánchez showed that there are at most five non-isotopic Seifert tori in the exterior of a hyperbolic knot. In this talk we address the case $n = 2$.