Exceptional Dehn Surgeries on Some Infinite Series of Hyperbolic Knots and Links

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-03 DOI:10.1007/s00009-024-02633-0

Alberto Cavicchioli, Fulvia Spaggiari

引用次数: 0

Abstract

We study closed connected orientable 3-manifolds obtained by Dehn surgery along the oriented components of a link, introduced and considered by Motegi and Song (2005) and Ichihara et al. (2008). For such manifolds, we find a finite balanced group presentation of the fundamental group and describe exceptional surgeries. This allows us to construct an infinite family of tunnel number one strongly invertible hyperbolic knots with three parameters, which admit toroidal surgeries and Seifert fibered surgeries. Among the obtained results, we mention that for every integer \(n >5\) there are infinitely many hyperbolic knots in the 3–sphere, whose \((n-2)\) and \((n+1)\)-surgeries are toroidal, and \((n-1)\) and n-surgeries are Seifert fibered.

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双曲结和链接的某些无穷序列上的异常 Dehn 手术

我们研究的是闭合连通的可定向三漫游流形，它是由 Motegi 和 Song（2005 年）以及 Ichihara 等人（2008 年）引入并考虑的沿着链路的定向分量进行 Dehn 手术得到的。对于这类流形，我们找到了基群的有限平衡群呈现，并描述了特殊的手术。这样，我们就可以构建一个具有三个参数的隧道数一强可逆双曲结的无穷系列，它们允许环状手术和塞弗特纤维手术。在得到的结果中，我们提到对于每一个整数（n >5），在3球中有无限多的双曲结，它们的（（n-2））和（（n+1））手术是环状的，而（（n-1））和n-手术是Seifert纤维的。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.