2016/03/19 by W. Edwin Clark, Clark, W. Edwin, Masahico Saito +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1603.06020
openalex publication_date 2016/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quandle 2-cocycles define invariants of classical and virtual knots, and extensions of quandles. We show that the quandle 2-cocycle invariant with respect to a non-trivial 2-cocycle is constant, or takes some other restricted form, for classical knots when the corresponding extensions satisfy certain algebraic conditions. In particular, if an abelian extension is a conjugation quandle, then the corresponding cocycle invariant is constant. Specific examples are presented from the list of connected quandles of order less than 48. Relations among various quandle epimorphisms involved are also examined.