同迹结的构造注释

Pub Date : 2020-10-26 DOI:10.32917/h2021005

Keiji Tagami

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引用次数: 3

摘要

结的$m$-迹是从$\mathbf｛B｝^4$获得的$4$-流形，方法是沿结连接一个带有$m$框架的$2$-柄。2015年，Abe、Jong、Luecke和Osoinach引入了一种技术，用相同的$$$-trace构造无限多个结，称为运算$[上百万]$。在本文中，我们证明了他们的技术可以用贡普夫和宫崎骏的可对偶图案来解释。此外，我们还表明，接受Teragaito提供的相同$4$-手术的结家族可以用手术$（\ast m）$来解释。

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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Notes on constructions of knots with the same trace

The $m$-trace of a knot is the $4$-manifold obtained from $\mathbf{B}^4$ by attaching a $2$-handle along the knot with $m$-framing. In 2015, Abe, Jong, Luecke and Osoinach introduced a technique to construct infinitely many knots with the same $m$-trace, which is called the operation $(\ast m)$. In this paper, we prove that their technique can be explained in terms of Gompf and Miyazaki's dualizable pattern. In addition, we show that the family of knots admitting the same $4$-surgery given by Teragaito can be explained by the operation $(\ast m)$.

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