Algebraic Properties of Quandle Extensions and Values of Cocycle Knot Invariants
Document Type
Article
Publication Date
2016
Keywords
Quandles, quandle cocycle invariants, abelian extensions of quandles
Digital Object Identifier (DOI)
https://doi.org/10.1142/S0218216516500802
Abstract
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.
Was this content written or created while at USF?
Yes
Citation / Publisher Attribution
Journal of Knot Theory and Its Ramifications, v. 25, issue 14, art. 1650080
Scholar Commons Citation
Clark, W. Edwin and Saito, Masahico, "Algebraic Properties of Quandle Extensions and Values of Cocycle Knot Invariants" (2016). Mathematics and Statistics Faculty Publications. 108.
https://digitalcommons.usf.edu/mth_facpub/108
