Algebraic Properties of Quandle Extensions and Values of Cocycle Knot Invariants

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 ce...

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Bibliographic Details
Published in:arXiv.org 2016-03
Main Authors: Clark, W Edwin, Saito, Masahico
Format: Article
Language:English
Subjects:
Algebra
Conjugation
Invariants
Knots
Online Access:Get full text
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Summary: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.
ISSN:2331-8422