Artin presentations of the trivial group and hyperbolic closed pure 3-braids

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-06-20 DOI:10.1016/j.topol.2024.108989

Lorena Armas-Sanabria , Jesús Rodríguez Viorato , E. Fanny Jasso-Hernández

引用次数: 0

Abstract

We consider a special class of framed links that arise from the hexatangle. Such links are introduced in [3], where it was also analyzed when the 3-manifold obtained after performing integral Dehn surgery on closed pure 3-braids is $S^{3}$ . In the present paper, we analyze the symmetries of the hexatangle and give a list of Artin n-presentations for the trivial group. These presentations correspond to the double-branched covers of the hexatangle that produce $S^{3}$ after Dehn surgery. Also, using a result of Birman and Menasco [4], we determine which closed pure 3-braids are hyperbolic.

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三元组和双曲封闭纯三元组的阿尔廷呈现

我们考虑的是由六边形产生的一类特殊的框架链接。在本文中，我们分析了六角形的对称性，并给出了三元组的阿廷呈现列表。这些呈现与德恩手术后产生的六角形双枝盖相对应。同时，利用比尔曼和梅纳斯科的一个结果，我们确定了哪些封闭的纯 3 边形是双曲的。

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.