论文标题
关于带相同痕迹结的结构的注释
Notes on constructions of knots with the same trace
论文作者
论文摘要
一个结的$ m $ - 跟踪是从$ \ mathbf {b}^4 $获得的$ 4 $ - manifold，它通过与$ M $ -M $ -FRAMING沿着结上的$ 2 $ - Handle。 2015年，安倍晋三，钟，卢克克和奥索纳赫推出了一种技术，以相同的$ m $ trace构建无限的许多结，这被称为操作$（\ ast m）$。在本文中，我们证明他们的技术可以用Gompf和Miyazaki的可划分模式来解释。此外，我们表明，可以通过操作$（\ ast m）$来解释Teragaito提供相同$ 4 $手术的结一家。
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 $(\ast m)$.
