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 $2$-handle along with $m$-framing. In 2015, Abe, Jong, Luecke and Osoinach introduced technique to construct infinitely many knots same $m$-trace, which called operation $(\ast m)$. this paper, we prove that their can be explained in terms Gompf Miyazaki's dualizable pattern. addition, show family admitting $4$-surgery given Teragaito