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- Title
Algebraic properties of quandle extensions and values of cocycle knot invariants.
- Authors
Clark, W. Edwin; Saito, Masahico
- 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 -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.
- Subjects
COCYCLES; KNOT theory; INVARIANTS (Mathematics); MORPHISMS (Mathematics); HOMOLOGICAL algebra
- Publication
Journal of Knot Theory & Its Ramifications, 2016, Vol 25, Issue 14, p-1
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216516500802