On annulus presentations, dualizable patterns and RGB-diagrams

Abstract

The $0$-trace of a knot is the $4$-manifold represented by the $0$-framing of the knot. In this manuscript, we survey methods constructing a pair of knots with diffeomorphic $0$-traces. In particular, we focus on Gompf-Miyazaki's dualizable pattern, Abe-Jong-Omae-Takeuchi's band presentation, and RGB-diagram given by Piccirillo and named by the author, and we draw the relations among these methods directly. As an application, we give a sufficient condition that two knots obtained by Abe-Jong-Omae-Takeuchi's method coincide.

22 pages, 24 figures,

Cited by in corpus (3)

• Notes on constructions of knots with the same trace
• Stein traces and characterizing slopes
• Knots with infinitely many non-characterizing slopes