Ribbon concordance of surface-knots via quandle cocycle invariants

2003/09/08 by J. Scott Carter, Carter, J. Scott, Masahico Saito +3
Computer Science · Mathematics · #55N99 #57M25 #57Q45 #57Q60 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:55N99 #msc:57M25 #msc:57Q45 #msc:57Q60 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0309150

14 pages, eight figures, interesting applications

arxiv created 2003/09/08 · openalex publication_date 2003/09/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give necessary conditions of a surface-knot to be ribbon concordant to another, by introducing a new variant of the cocycle invariant of surface-knots in addition to using the invariant already known. We demonstrate that twist-spins of some torus knots are not ribbon concordant to their orientation reversed images.

Citations

• A classifying invariant of knots, the knot quandle

Related

• Computations of Quandle Cocycle Invariants of Knotted Curves and Surfaces
• Quasi-ribbon but non-ribbon surface-link of trivial components
• Symmetric quandle colorings and ribbon concordance
• Quandle Cohomology and State-sum Invariants of Knotted Curves and Surfaces
• Diagrammatic Computations for Quandles and Cocycle Knot Invariants