Symmetric quandle colorings and ribbon concordance

2022/12/19 by Cazet, Nicholas
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2212.09218

Abstract

A quandle can always trivially color an orientable surface-link. This note shows that the surface-link 10₁^-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 8₁^-1,-1 that does admit a coloring by the same symmetric dihedral quandle.

Related

• Quandles versus symmetric quandles for oriented links
• Ribbon concordance of surface-knots via quandle cocycle invariants
• Symmetric Extensions of Dihedral Quandles and Triple Points of Non-orientable Surfaces
• Quandle colorings vs. biquandle colorings
• Computations of quandle cocyle invariants of surface-links using marked graph diagrams