Positive links with arrangements of pseudocircles as shadows

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-06-17 DOI:10.1016/j.topol.2024.108999

Carolina Medina , Santino Ramírez , Jorge L. Ramírez-Alfonsín , Gelasio Salazar

引用次数: 0

Abstract

An arrangement of pseudocircles $A$ is a collection of Jordan curves in the plane that pairwise intersect (transversally) at exactly two points. How many non-equivalent links have $A$ as their shadow? Motivated by this question, we study the number of non-equivalent positive oriented links that have an arrangement of pseudocircles as their shadow. We give sharp estimates on this number when $A$ is one of the three unavoidable arrangements of pseudocircles.

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与作为阴影的伪圆排列的积极联系

假圆的排列 A 是平面内恰好两点成对相交（横交）的约旦曲线的集合。有多少非等价链接以 A 为影？受这一问题的启发，我们研究了以伪圆排列作为其阴影的非等价正向链接的数量。当 A 是三种不可避免的伪圆排列之一时，我们给出了关于这一数目的精确估计。

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.