We discuss degree-preserving crossing change on Khovanov homology in terms of cobordisms. Namely, using Bar-Natan's formalism of Khovanov homology, we investigate a sum of cobordisms that yields a morphism between complexes of two diagrams related by a change of crossing, which we call the “genus-one morphism.” We prove that the morphism is invariant under the moves of double points in tangle diagrams. As a consequence, in the spirit of Vassiliev theory, taking iterated mapping cones, we obtain invariants for singular tangles that extend sl(2) tangle homologies; examples include Lee homology, Bar-Natan homology, and Naot's universal Khovanov homology as well as Khovanov homology with arbitrary coefficients. We also verify that the invariant satisfies categorified analogues of Vassiliev skein relation and the FI relation.

我们讨论了用钴硼酸盐对科沃诺夫同源性进行保度杂交的变化。即，使用巴尔·纳坦（Bar-Natan）的Khovanov同源性形式学，我们研究了cobordisms的总和，该合子在两个图的复合物之间产生了形态变化，该形态通过交叉的变化而相关，我们称之为“属一形态学”。我们证明了在缠结图中双点运动下，态射是不变的。结果，本着Vassiliev理论的精神，采用迭代映射锥，我们获得了奇异缠结的不变量，这些奇异缠结扩展了sl（2）纠缠同构；示例包括Lee同源性，Bar-Natan同源性和Naot通用Khovanov同源性以及具有任意系数的Khovanov同源性。我们还验证了不变量满足Vassiliev绞链关系和FI关系的分类类似物。