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

Román Aranda; Enrique Ramírez-Losada; Jesús Rodríguez-Viorato

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arXiv · 2304.09312

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

Román Aranda·Enrique Ramírez-Losada·Jesús Rodríguez-Viorato

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Abstract

This paper continues 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-S\'anchez showed that there are at most five non-isotopic 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 non-isotopic, nested, essential 2-holed tori in the complement of every hyperbolic knot.

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Román Aranda, Enrique Ramírez-Losada, Jesús Rodríguez-Viorato. 2023-04-18. A bound on the number of twice-punctured tori in a knot exterior. https://arxiv.org/abs/2304.09312

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