On annulus presentations, dualizable patterns and RGB-diagrams
Geometric Topology
2023-06-30 v3
Abstract
The -trace of a knot is the -manifold represented by the -framing of the knot. In this manuscript, we survey methods constructing a pair of knots with diffeomorphic -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,