AI 中文总结
研究在\(\mathbb{R}^4\)中构造不可约奇异恰当纽结曲面的无穷族，通过给出奇异开 2 - 柄的灵活构造，利用双分支覆盖的相关性质区分奇异曲面，并构造新的拓扑切片链族，解决戈姆夫的相关问题。
AI 中文摘要
我们在\(\mathbb{R}^4\)中构造了不可约奇异恰当纽结曲面的无穷族，这在戈姆夫的一个问题上取得了进展。这里不可约意味着这些曲面不是标准曲面与奇异平面的端和。为证明拓扑等价性，我们给出了奇异开 2 - 柄的高度灵活构造，推广了文献中的几个类似构造。我们通过它们的双分支覆盖的亏格函数和端弗洛尔同调区分奇异曲面。通过进一步研究这些广义柄，我们构造了一个新的拓扑切片链族。
英文摘要
We construct infinite families of irreducible exotic proper knotted surfaces in $\mathbb{R}^4$, making progress on a question of Gompf. Here irreducible means these surfaces are not end-sums of standard surfaces with exotic planes. To prove the topological equivalence, we give a highly flexible construction of exotic open 2-handles, which generalizes several similar constructions in the literature. We distinguish exotic surfaces through the genus functions and end Floer homology of their double branched covers. By studying these generalized handles further, we construct a new family of topologically slice links.
Comments32 pages, 24 figures. Section 2 updated. Comments welcome!
