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

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-05-07 DOI:10.1016/j.topol.2024.108938

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

引用次数: 0

Abstract

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.

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论双曲结外部嵌套两次穿刺环的数量

本文延续了本木（Motegi）提出的关于 S3 中双曲结的补集中的非异位本质 n 切分环的数量的普遍界限的计划。对于 n=1 的情况，Valdez-Sánchez 证明了双曲结外部最多有五个非异位的 Seifert 转矩。本文将讨论 n=2 的情况。我们证明了在每个双曲结的补集中最多有六个非异位、嵌套、本质 2 孔环。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.