论文标题
签名的双重分属的下限
A lower bound for the doubly slice genus from signatures
论文作者
论文摘要
三个球中的结的双重切片属是在4个球体中不结结的定向表面中结的最小属，而结成结为横截面。我们使用结的经典特征功能为双重切片属提供新的下限。由于C. McDonald，我们将其与上限结合在一起，以证明对于每个非负整数$ n $，都有一个结，slice和双重切片属之间的差异正好是$ n $，可以完善W. Chen的结果。
The doubly slice genus of a knot in the 3-sphere is the minimal genus among unknotted orientable surfaces in the 4-sphere for which the knot arises as a cross-section. We use the classical signature function of the knot to give a new lower bound for the doubly slice genus. We combine this with an upper bound due to C. McDonald to prove that for every nonnegative integer $N$ there is a knot where the difference between the slice and doubly slice genus is exactly $N$, refining a result of W. Chen which says this difference can be arbitrarily large.
