On the number of nested twice-punctured tori in a hyperbolic knot exterior.

This paper continues a program due to Motegi regarding universal bounds for the number of nonisotopic 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 nonisotopic Seifert tori in the exterior of a hyperbolic knot. In this paper, we address the case n = 2. We show that there are at most six nonisotopic, nested, essential 2-holed tori in the complement of every hyperbolic knot. [ABSTRACT FROM AUTHOR]