相对Khovanov-Jacobsson类
Relative Khovanov-Jacobsson classes
摘要：
对于$4$ -球中的光滑、紧致、有向、适当嵌入的曲面，我们从其边界链的Khovanov同调定义了其保边界合痕类的一个不变量。以前的工作表明，当边界链接是空的，这个不变量是由曲面的亏格。我们表明，这种相对不变式：可以阻碍sliceness的结;检测一对切片$9_{46}$ ;不妨碍检测连接和打结$2$ -领域。
英文摘要：
To a smooth, compact, oriented, properly-embedded surface in the $4$-ball, we define an invariant of its boundary-preserving isotopy class from the Khovanov homology of its boundary link. Previous work showed that when the boundary link is empty, this invariant is determined by the genus of the surface. We show that this relative invariant: can obstruct sliceness of knots; detects a pair of slices for $9_{46}$; is not hindered by detecting connected sums with knotted $2$-spheres.
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