意想不到的基本表面在扭曲的环状结的外部之间

IF 0.6 3区数学 Q3 MATHEMATICS

Algebraic and Geometric Topology Pub Date : 2020-12-17 DOI:10.2140/agt.2022.22.3965

Thiago de Paiva

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引用次数: 8

摘要

扭环结K(p, q;R, s)是通过对R个相邻的(p, q)环面结进行s个完整扭转而得到的。本文回答了与扭曲环面结外表面的基本曲面有关的两个问题。也就是说，我们证明存在大于2的素数r，使得K(p, q;r, s)在它们的外部包含封闭本质面，回答了森本和山田的一个问题。此外，Morimoto还询问了是否所有外部具有基本环面的扭曲环面结都属于两种类型之一。我们发现了一个以前未知的新的无限家族。

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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Unexpected essential surfaces among exteriors of twisted torus knots

The twisted torus knots K(p, q; r, s) are obtained by performing a sequence of s full twists on r adjacent strands of (p, q)-torus knots. In this paper, we answer two questions related to essential surfaces in the exteriors of twisted torus knots. Namely, we show there are prime numbers r greater than 2 such that K(p, q; r, s) contain closed essential surface in their exterior, answering a question of Morimoto and Yamada. Additionally, Morimoto asked whether all twisted torus knots with essential tori in the exterior fit into one of two families. We find a new infinite family that was previously unknown.

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来源期刊

Algebraic and Geometric Topology 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebraic and Geometric Topology is a fully refereed journal covering all of topology, broadly understood.