AI 中文总结
本文在4-流形中构造了无穷多个经单次稳定化（与S^2 x S^2连通和）后变为可光滑化的不可光滑化嵌入曲面，并给出稳定化次数为1的充分条件，还证明K3曲面中存在此类曲面其拓扑同位类含无穷多个非光滑同位的光滑代表。
AI 中文摘要
在本文中，我们找到了4-流形中无穷多个不可光滑化的嵌入曲面的例子，这些曲面在与S^2 x S^2作连通和后变为可光滑化。据作者所知，此前尚未发现此类例子。在[CK25]中，Cha和Kim询问了将不可光滑化曲面变为可光滑化曲面所需的最少稳定化次数。我们提供了确保该次数为1的充分条件。此外，我们证明在K3曲面中存在一个不可光滑化曲面，经过单次稳定化后，其拓扑同位类包含无穷多个光滑代表，且这些代表两两不是光滑同位的。
英文摘要
In this paper, we find infinitely many examples of nonsmoothable embedded surfaces in a 4-manifold that become smoothable after taking the connected sum with S^2 x S^2. To the author's knowledge, no such examples have previously been discovered. In [CK25], Cha and Kim asked for the minimal number of stabilizations required to turn a nonsmoothable surface into a smoothable one. We provide sufficient conditions ensuring that this number is 1. In addition, we show that there is a nonsmoothable surface in a K3 surface such that, after a single stabilization, its topological isotopy class contains infinitely many smooth representatives that are pairwise not smoothly isotopic.
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