论文标题
对于具有边界的外来表面，一个稳定不够
For Exotic Surfaces with Boundary, One Stabilization is Not Enough
论文作者
论文摘要
Baykur-Sunukjian的结果表明，在有限数量的内部稳定值（即将管子连接到表面上），4个manifold中的同源表面成为同位素。一个自然的问题是，在表面成为同位素之前需要进行多少稳定。特别是给定异国情调的表面，单个稳定始终足以使这对同位素平滑？我们通过研究随着卫星操作的边界变化的表面之间的稳定距离如何回答这个问题。使用一系列的浮动理论技术，我们表明四球中有外来的磁盘，它们的稳定距离任意较大，这给出了“一个人不够”的四个球中外来行为的第一个例子。
A result of Baykur-Sunukjian states that homologous surfaces in a 4-manifold become isotopic after a finite number of internal stabilizations, i.e. attaching tubes to the surfaces. A natural question is how many stabilizations are needed before the surfaces become isotopic. In particular, given an exotic pair of surfaces, is a single stabilization always enough to make the pair smoothly isotopic? We answer this question by studying how the stabilization distance between surfaces with boundary changes with respect to satellite operations. Using a range of Floer theoretic techniques, we show that there are exotic disks in the four-ball which have arbitrarily large stabilization distance, giving the first examples of exotic behavior in the four-ball for which "one is not enough".
