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The structure of biquandle brackets
Journal of Knot Theory and Its Ramifications ( IF 0.5 ) Pub Date : 2020-05-18 , DOI: 10.1142/s021821652050042x
Will Hoffer 1 , Adu Vengal 2 , Vilas Winstein 2
Affiliation  

In their paper entitled “Quantum Enhancements and Biquandle Brackets”, Nelson, Orrison, and Rivera introduced biquandle brackets, which are customized skein invariants for biquandle-colored links. We prove herein that if a biquandle bracket [Formula: see text] is the pointwise product of the pair of functions [Formula: see text] with a function [Formula: see text], then [Formula: see text] is also a biquandle bracket if and only if [Formula: see text] is a biquandle 2-cocycle (up to a constant multiple). As an application, we show that a new invariant introduced by Yang factors in this way, which allows us to show that the new invariant is in fact equivalent to the Jones polynomial on knots. Additionally, we provide a few new results about the structure of biquandle brackets and their relationship with biquandle 2-cocycles.

中文翻译:

双组括号的结构

在他们题为“Quantum Enhancements and Biquandle Brackets”的论文中,Nelson、Orrison 和 Rivera 介绍了 biquandle 括号,它们是用于 biquandle 彩色链接的定制绞线不变量。我们在此证明,如果双组括号 [Formula: see text] 是函数对 [Formula: see text] 与函数 [Formula: see text] 的逐点乘积,则 [Formula: see text] 也是双组括号当且仅当 [Formula: see text] 是 biquandle 2-cocycle(最多为常数倍)。作为一个应用,我们证明了杨因子以这种方式引入的新不变量,这使我们能够证明新不变量实际上等价于节点上的琼斯多项式。此外,我们提供了一些关于双四方括号的结构及其与双四方2-cocycles的关系的新结果。
更新日期:2020-05-18
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