论文标题
在不确定的4个manifolds中的准阳性结的切片属上
On the slice genus of quasipositive knots in indefinite 4-manifolds
论文作者
论文摘要
令$ x $为封闭的无限$ 4 $ - manifold，$ b _+（x）= 3 \; （{\ rm mod} \; 4）$，并且具有非逐渐变化的mod $ 2 $ seiberg- witten不变性。我们证明，在$ x \ setminus b^4 $中，在适当嵌入的表面的属上证明了一个新的下限，代表给定同源性类别，并且具有边界的准稳态结$ k \ subset s^3 $。在无效的情况下，我们的不平等意味着这种表面的最小属等于$ k $的切片属。如果$ x $是符合性的，那么对于任何可以用符号表面表示的同源类别的同源类别，我们的下限与最小属的不同。在此过程中，我们还证明了与负面自我交流类别的$ 4 $ manifolds的接落不平等的扩展，而无需$ x $简单的类型。
Let $X$ be a closed indefinite $4$-manifold with $b_+(X) = 3 \; ({\rm mod} \; 4)$ and with non-vanishing mod $2$ Seiberg--Witten invariants. We prove a new lower bound on the genus of a properly embedded surface in $X \setminus B^4$ representing a given homology class and with boundary a quasipositive knot $K \subset S^3$. In the null-homologous case our inequality implies that the minimal genus of such a surface is equal to the slice genus of $K$. If $X$ is symplectic then our lower bound differs from the minimal genus by at most $1$ for any homology class that can be represented by a symplectic surface. Along the way, we also prove an extension of the adjunction inequality for closed $4$-manifolds to classes of negative self-intersection without requiring $X$ to be of simple type.
