English

On annulus presentations, dualizable patterns and RGB-diagrams

Geometric Topology 2023-06-30 v3

Abstract

The 00-trace of a knot is the 44-manifold represented by the 00-framing of the knot. In this manuscript, we survey methods constructing a pair of knots with diffeomorphic 00-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.

Cite

@article{arxiv.2010.13283,
  title  = {On annulus presentations, dualizable patterns and RGB-diagrams},
  author = {Keiji Tagami},
  journal= {arXiv preprint arXiv:2010.13283},
  year   = {2023}
}

Comments

22 pages, 24 figures,

R2 v1 2026-06-23T19:38:21.613Z