分类Biquandle托槽
Categorifying Biquandle Brackets
摘要：
在他们题为“Quantum Enhancements and Biquandle Brackets”的论文中，Nelson、Orrison和Rivera介绍了biquandle Brackets，这是用于biquandle颜色链接的定制的绞链不变量。这些不变量推广了琼斯多项式，琼斯多项式由Khovanov同调分类。在论文的最后，Nelson、Orrison和Rivera询问了Khovanov同调的方法是否可以扩展到双括号的分类。我们在这里概述了Khovanov同源式的建设，是一种尝试，以获得这样一个分类的biquandle括号。由此产生的结不变量推广了Khovanov同调，但双括号并不总是可恢复的，这意味着该结构不是双括号的真正分类。然而，这种构造确实导致了一个定义，给出了一个与一个双量子括号相关联的“规范”双量子2-上循环，据作者所知，这是以前不知道的。
英文摘要：
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. These invariants generalize the Jones polynomial, which is categorified by Khovanov homology. At the end of their paper, Nelson, Orrison, and Rivera asked if the methods of Khovanov homology could be extended to obtain a categorification of biquandle brackets. We outline herein a Khovanov homology-style construction that is an attempt to obtain such a categorification of biquandle brackets. The resulting knot invariant generalizes Khovanov homology, but the biquandle bracket is not always recoverable, meaning the construction is not a true categorification of biquandle brackets. However, the construction does lead to a definition that gives a "canonical" biquandle 2-cocycle associated to a biquandle bracket, which, to the authors' knowledge, was not previously known.
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