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arXiv · 2010.13292

Notes on constructions of knots with the same trace

Keiji Tagami
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Abstract

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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Keiji Tagami. 2020-10-26. Notes on constructions of knots with the same trace. https://doi.org/10.32917/h2021005

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