Title

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

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