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Algebraic properties of quandle extensions and values of cocycle knot invariants

W. Edwin Clark

Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

E-mail Address: wclark@mail.usf.edu

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and

Masahico Saito

http://orcid.org/0000-0003-0795-8548

Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

E-mail Address: saito@math.usf.edu

Corresponding author.

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https://doi.org/10.1142/S0218216516500802Cited by:9 (Source: Crossref)

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.

Keywords:

AMSC: 57M25

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