论文标题
在$ \ mathfrak {sl} _2 $ Tangle同源性和分类Vassiliev skein Relation上的COBORDISM意识到交叉变化
A cobordism realizing crossing change on $\mathfrak{sl}_2$ tangle homology and a categorified Vassiliev skein relation
论文作者
论文摘要
在本文中，我们讨论了0学位的跨越同源性的交叉变化。也就是说，使用Bar-Natan对Khovanov同源性的形式主义，我们引入了一系列的恢复主义，这些总和对两个杂交变化的复合物产生了形态，我们称之为“属属形态”。事实证明，在纠缠图中双点的移动下，形态是不变的。结果，本着瓦西里耶夫理论的精神，采用了迭代的映射锥体，我们获得了一个奇异缠结的不变性，从而扩展了SL（2）缠结同源性。例子包括Lee同源性，Bar-Natan同源性和NAOT的普遍Khovanov同源性以及具有任意系数的Khovanov同源性。我们还验证了不变的满足Vassiliev skein关系和FI关系的分类类似物。
In this paper, we discuss degree 0 crossing change on Khovanov homology in terms of cobordisms. Namely, using Bar-Natan's formalism of Khovanov homology, we introduce a sum of cobordisms that yields a morphism on complexes of two diagrams of crossing change, which we call the "genus-one morphism." It is proved 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 an invariant for singular tangles that extending sl(2) tangle homology; 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.
