Symmetric quandle colorings and ribbon concordance

TL;DR

This paper investigates how symmetric dihedral quandle colorings can obstruct ribbon concordance between certain surface-links, providing new insights into their topological properties.

Contribution

It demonstrates that specific surface-links cannot be colored by a symmetric dihedral quandle, revealing new obstructions to ribbon concordance.

Findings

The surface-link 10_1^{-1,-1} cannot be colored by the symmetric dihedral quandle of order 4.

This coloring obstruction prevents a generalized ribbon concordance with another link.

The work links quandle colorings to topological invariants of surface-links.

Abstract

A quandle can always trivially color an orientable surface-link. This note shows that the surface-link $10_1^{-1,-1}$ of Yoshikawa's table cannot be colored by a symmetric dihedral quandle of order 4, and explains how this obstructs a generalized ribbon concordance between another link of two projective planes $8_1^{-1,-1}$ that does admit a coloring by the same symmetric dihedral quandle.