论文标题
不确定四元中的相对属边界
Relative genus bounds in indefinite four-manifolds
论文作者
论文摘要
鉴于封闭的四个manifold $ x $，带有不确定的交点表格，我们认为在$ x \ setminus $ int $（b^4）$中平滑嵌入了表面，带有边界A结$ k \ subset s^3 $。我们提供了几种方法来绑定固定同源性类别中此类表面的属。我们的工具包括邻接不平等和$ 10/8 + 4 $定理。特别是，我们在四个manifold中提出了一个打结的障碍物（即，即无效的磁盘），并表明H-Slice结组可以在封闭的$ 4 $ manifolds上检测出奇异的平滑结构。
Given a closed four-manifold $X$ with an indefinite intersection form, we consider smoothly embedded surfaces in $X \setminus $int$(B^4)$, with boundary a knot $K \subset S^3$. We give several methods to bound the genus of such surfaces in a fixed homology class. Our tools include adjunction inequalities and the $10/8 + 4$ theorem. In particular, we present obstructions to a knot being H-slice (that is, bounding a null-homologous disk) in a four-manifold and show that the set of H-slice knots can detect exotic smooth structures on closed $4$-manifolds.
