Splittings of tangles and spatial graphs

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-08-20 DOI:10.1016/j.topol.2024.109042

Erica Flapan , Hugh Howards

引用次数: 0

Abstract

Menasco proved that if G is a reduced, alternating, connected diagram of a link L and G is prime then L is prime. This surprising and important result has been generalized to other classes of links, as well as to tangles and spatial graphs. After exploring some issues with previous results, we obtain new splitting results for tangles and spatial graphs.

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纠结和空间图的分裂

梅纳斯科证明，如果 G 是链接 L 的还原、交替、连通图，并且 G 是素数，那么 L 就是素数。这一惊人而重要的结果已被推广到其他类别的链接以及缠结和空间图。在探讨了之前结果的一些问题之后，我们得到了缠结图和空间图表的新分裂结果。

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.