Symmetric quandle colorings and ribbon concordance
Nicholas Cazet

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 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 that does admit a coloring by the same symmetric dihedral quandle.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory
