AI 中文总结
研究\(B^4\)中光滑定向恰当嵌入曲面边缘手术对考夫曼同调的影响，通过局部环面替换操作，结合已有工作得出奇异曲面，利用考夫曼缠结千层饼模给出两个证明。
AI 中文摘要
我们证明，在\(B^4\)中对一个光滑、定向、恰当嵌入的曲面进行边缘手术，不会改变该曲面在考夫曼同调上诱导的映射，回答了海登和桑德伯格提出的一个问题。更一般地，对于一类我们称为局部环面替换的局部手术操作，同样的不敏感性也成立。结合海登 - 桑德伯格的工作，该结果产生了\(B^4\)中不能通过任何局部环面替换序列相关联的奇异曲面。我们给出了两个证明，都本质上利用了考夫曼缠结千层饼模。
英文摘要
We show that rim surgery on a smooth, oriented, properly embedded surface in $B^4$ does not change the map on Khovanov homology induced by the surface, answering a question raised by Hayden and Sundber. More generally, the same insensitivity holds for a class of local surgery operations that we call local annulus replacements. Combined with the work of Hayden--Sundberg, this result yields exotic pairs of surfaces in $B^4$ that cannot be related by any sequence of local annulus replacements. We give two proofs, both making essential use of Khovanov skein lasagna modules.
Comments8 pages, 2 figures
