Notes on constructions of knots with the same trace

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 $(\ast m)$.

12 pages, 7 figures

References in corpus (2)

• On annulus presentations, dualizable patterns and RGB-diagrams
• Knots with infinitely many non-characterizing slopes

Cited by in corpus (2)

• Stein traces and characterizing slopes
• From zero surgeries to candidates for exotic definite four-manifolds