论文标题
Khovanov的同源性和分裂链接之间的COBORDISM
Khovanov homology and cobordisms between split links
论文作者
论文摘要
在本文中，我们研究了Khovanov函子对表面四维链接的敏感性。我们证明，如果$ l $和$ l'$是分链链接，而$ c $是$ l $ l $和$ l'$之间的共同体，那是$ l $的组件（但可能是链接的）共同体（但可能是链接的）结合的结合。组件之间的链接。作为推论，我们证明了强烈同质的 - ribbon一致性（即，可以仅用1和2个手柄构建补充的一致性）会引起对Khovanov同源性的注入，这概述了第二作者和Zemke的结果。此外，我们表明，非分类链接不能与分裂链接相一致。
In this paper, we study the (in)sensitivity of the Khovanov functor to four-dimensional linking of surfaces. We prove that if $L$ and $L'$ are split links, and $C$ is a cobordism between $L$ and $L'$ that is the union of disjoint (but possibly linked) cobordisms between the components of $L$ and the components of $L'$, then the map on Khovanov homology induced by $C$ is completely determined by the maps induced by the individual components of $C$ and does not detect the linking between the components. As a corollary, we prove that a strongly homotopy-ribbon concordance (i.e., a concordance whose complement can be built with only 1- and 2-handles) induces an injection on Khovanov homology, which generalizes a result of the second author and Zemke. Additionally, we show that a non-split link cannot be ribbon concordant to a split link.
