A colored Khovanov bicomplex
A colored Khovanov bicomplex
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彩色霍瓦诺夫双复合体
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
N. Ito
中科院分区：
文献类型：
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作者：
N. Ito
在本文中，我们证明了一个三阶khovanov型双复的存在性（定理1.2）。与该双络合物相关的总络合物的梯度欧拉特征是连杆的彩色琼斯多项式。双络合物的第一个等级是同源的，来自于连接的电缆（即，用几个平行的链代替连接的一条链）；第二次分级与普通Khovanov同调的同调分级有关；最后，第三阶由微分保留，对应于有色琼斯多项式中变量的阶数。特别地，我们介绍了一种直接从大型布线链路图中提取小型布线链路图的方法（定理3.2）。这是arXiv:0907.5247的改进版本。
In this note, we prove the existence of a tri-graded Khovanov-type bicomplex (Theorem 1.2). The graded Euler characteristic of the total complex associated with this bicomplex is the colored Jones polynomial of a link. The first grading of the bicomplex is a homological one derived from cabling of the link (i.e., replacing a strand of the link with several parallel strands); the second grading is related to the homological grading of ordinary Khovanov homology; finally, the third grading is preserved by the differentials, and corresponds to the degree of the variable in the colored Jones polynomial. In particular, we introduce a way to take a small cabling link diagram directly from a big cabling link diagram (Theorem 3.2). This is a refined version of arXiv:0907.5247.
Khovanov 同源性的链同伦图
影响因子：
0.5
作者：
N. Ito
通讯作者：
N. Ito