论文标题
彩色的Khovanov Bicomplex
A colored Khovanov bicomplex
论文作者
论文摘要
在本说明中，我们证明了三个级别的khovanov型双孔（定理1.2）的存在。与该双色相关的总复合物的分级欧拉特征是链接的彩色琼斯多项式。双色的第一个分级是源自链路的电缆（即，用几个平行线代替链路）衍生出的同源性。第二个评分与普通Khovanov同源性的同源分级有关。最后，第三个分级由差分保留，对应于彩色琼斯多项式中的变量程度。特别是，我们引入了一种直接从大型电缆链路图（定理3.2）中获取小型电缆链路图的方法。这是Arxiv的精制版本：0907.5247。
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.
