论文标题
打开21节在K3中是切片
Unknotting number 21 knots are slice in K3
论文作者
论文摘要
We prove that all knots with unknotting number at most 21 are smoothly slice in the K3 surface. We also prove a more general statement for 4-manifolds that contain a plumbing tree of spheres.我们的策略是基于一种灵活的方法，可以通过在嵌入树木的邻居上进行管道来删除4个manifolds中浸泡的表面的双重点。作为副产品，我们恢复了诺曼和铃木的经典结果，即每个结都以$ s^2 \ times s^2 $和$ \ mathbb {cp}^2 \＃\＃\ edline {\ mathbb {cp {cp}^2} $。
We prove that all knots with unknotting number at most 21 are smoothly slice in the K3 surface. We also prove a more general statement for 4-manifolds that contain a plumbing tree of spheres. Our strategy is based on a flexible method to remove double points of immersed surfaces in 4-manifolds by tubing over neighbourhoods of embedded trees. As a byproduct, we recover a classical result of Norman and Suzuki that every knot is smoothly slice in $S^2 \times S^2$ and in $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$.
