Clark W Edwin, Saito Masahico
Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA.
J Knot Theory Ramif. 2016 Dec;25(14). doi: 10.1142/s0218216516500802. Epub 2016 Oct 11.
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.
quandle 2 - 上循环定义了经典纽结和虚拟纽结以及quandle的扩张的不变量。我们证明，当相应的扩张满足某些代数条件时，对于经典纽结，相对于非平凡2 - 上循环的quandle 2 - 上循环不变量是常数，或者具有其他某种受限形式。特别地，如果一个阿贝尔扩张是共轭quandle，那么相应的上循环不变量是常数。从阶小于48的连通quandle列表中给出了具体例子。还研究了所涉及的各种quandle满同态之间的关系。
