Khovanov homology and cobordisms between split links
Khovanov homology and cobordisms between split links
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分裂链接之间的霍瓦诺夫同源性和共边
作者：
O. S. Gujral;A. Levine
在本文中，我们研究了Khovanov函子对4维曲面链接的（不）敏感性。我们证明了：如果L$L$和L′$L^{\prime }$是分裂环，C$C$是L$L$和L′$L^{\prime }$之间的协边，即不相交的并L$L$的分量和L′$L^{\prime }$的分量之间的（但可能是相连的）配边，那么由C$C$诱导的Khovanov同源性上的映射完全由C$C$的各个组分诱导的映射决定，并且不检测组分之间的连接。作为推论，我们证明了强同伦带协调（即，其补集可以仅用1-和2-柄建立的协调）诱导Khovanov同调的注入，这推广了第二作者和Zemke的结果。此外，我们表明，一个非分裂链接不能带状一致的分裂链接。
In this paper, we study the (in)sensitivity of the Khovanov functor to 4‐dimensional linking of surfaces. We prove that if L$L$ and L′$L^{\prime }$ are split links, and C$C$ is a cobordism between L$L$ and L′$L^{\prime }$ that is the union of disjoint (but possibly linked) cobordisms between the components of L$L$ and the components of L′$L^{\prime }$ , then the map on Khovanov homology induced by C$C$ is completely determined by the maps induced by the individual components of C$C$ and does not detect the linking between the components. As a corollary, we prove that a strongly homotopy–ribbon concordance (that is, 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.
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带状同源配边
影响因子：
1.7
作者：
Daemi, Aliakbar;Lidman, Tye;Vela-Vick, David Shea;Wong, C.-M. Michael
通讯作者：
Wong, C.-M. Michael
影响因子：
0.7
作者：
.Ilker S. Yuce-Ilker-S.-Yuce-102800584
通讯作者：
.Ilker S. Yuce-Ilker-S.-Yuce-102800584
Knot Floer 同源性阻碍了丝带一致性
影响因子：
4.9
作者：
Zemke, null
通讯作者：
Zemke, null
霍瓦诺夫同源性和带状索引
影响因子：
0.9
作者：
Levine, Adam Simon;Zemke, Ian
通讯作者：
Zemke, Ian
链接弗洛尔同源性中的链接共边性和函子性
影响因子：
1.1
作者：
Zemke, Ian
通讯作者：
Zemke, Ian