Divides with cusps and symmetric links

IF 0.5 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2025-03-01 Epub Date: 2025-01-13 DOI:10.1016/j.topol.2025.109207

Sakumi Sugawara

引用次数: 0

Abstract

A divide with cusps is the image of a proper generic immersion from finite intervals and circles into a 2-disk which allows to have cusps. A divide with cusps is a generalization of the notion of the divide which is introduced by A'Campo. From a divide with cusps, we can define the associated link in

S^{3}

. In this paper, we give the characterization of links in

S^{3}

which can be described as the associated link of a divide with cusps. In particular, we prove that every strongly invertible link and 2-periodic link can be described as the link of a divide with cusps.

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用尖头和对称链接划分

有尖点的分割是一个适当的一般浸入的图像，从有限的间隔和圆到一个允许有尖点的2盘。尖分法是对阿坎波提出的分法概念的概括。我们可以在S3中定义带有尖点的分隔。在本文中，我们给出了S3中链接的表征，这些链接可以被描述为带有尖端的分割的关联链接。特别地，我们证明了每一个强可逆环和每一个2周期环都可以被描述为带尖分环的环。

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.

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