English

Symmetric quandle colorings and ribbon concordance

Geometric Topology 2024-06-05 v2

Abstract

A quandle can always trivially color an orientable surface-link. This note shows that the surface-link 1011,110_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 811,18_1^{-1,-1} that does admit a coloring by the same symmetric dihedral quandle.

Keywords

Cite

@article{arxiv.2212.09218,
  title  = {Symmetric quandle colorings and ribbon concordance},
  author = {Nicholas Cazet},
  journal= {arXiv preprint arXiv:2212.09218},
  year   = {2024}
}