论文标题
分类双方括号
Categorifying Biquandle Brackets
论文作者
论文摘要
纳尔逊（Nelson），奥里森（Orrison）和里维拉（Rivera）在其题为“量子增强和双Quandle括号”的论文中引入了Biquandle括号，它们是定制的用于双Quandle颜色链接的链球化型不变性。这些不变的人概括了琼斯多项式，该多项式由Khovanov同源性分类。在论文的最后，纳尔逊，奥里森和里维拉询问了Khovanov同源性的方法是否可以扩展以获取Biquandle括号的分类。 我们在这里概述了Khovanov同源风格的结构，该结构是试图获得Biquandle括号的这种分类。由此产生的结不变概括了Khovanov的同源性，但是双方支架并不总是可恢复的，这意味着构造并不是对双方括号的真正分类。但是，该结构确实导致了一个定义，该定义给出了与Biquandle支架相关的“规范”的Biquandle 2 cocycle，据作者所知，该圆环以前尚不清楚。
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.
