论文标题
单个稳定后K3＃K3上的Dehn Twist的同位素
Isotopy of the Dehn twist on K3#K3 after a single stabilization
论文作者
论文摘要
Kronheimer-Mrowka最近证明，沿$ K3 \＃k3 $的3个球沿3个球的Dehn Twist对身份的同位素并不顺利。这为4个manifolds的自我呈现形态提供了一个新的例子，这些示例是对拓扑类别的身份同位素同位素的同位素，但并非如此。 （第一个这样的例子是Ruberman给出的。）在本文中，我们使用PIN（2） - Equivariant Bauer-Furuta不变性，以表明即使在单个稳定后，Dehn Twist也不是对身份的同位素平稳的（与$ s^{2} \ times s^times s^{2} $相连的汇总（连接）。这给出了简单地连接的平滑4个manifolds上的外来现象的第一个例子，这些现象在单个稳定后不会消失。
Kronheimer-Mrowka recently proved that the Dehn twist along a 3-sphere in the neck of $K3\#K3$ is not smoothly isotopic to the identity. This provides a new example of self-diffeomorphisms on 4-manifolds that are isotopic to the identity in the topological category but not smoothly so. (The first such examples were given by Ruberman.) In this paper, we use the Pin(2)-equivariant Bauer-Furuta invariant to show that this Dehn twist is not smoothly isotopic to the identity even after a single stabilization (connected summing with the identity map on $S^{2}\times S^{2}$). This gives the first example of exotic phenomena on simply connected smooth 4-manifolds that do not disappear after a single stabilization.
