论文标题
4球中的2次球形的打开数字
Unknotting numbers of 2-spheres in the 4-sphere
论文作者
论文摘要
我们比较了在4个球体中2个小时的两个自然产生的概念：即获得未结织的表面所需的1个手柄稳定数量的最小数量，而定期同质拷贝需要的惠特尼动作数量最少才能达到未开关的2球。我们将这些不变性分别称为稳定数和球体的卡森 - 惠特尼数。使用代数和几何技术，我们表明稳定数的限制比Casson-Whitney数字多。我们还提供了这些不变性相等的球体家庭，以及它们与众不同的家庭。此外，我们为不变的范围提供了其他界限，其非依恋性的具体示例以及对经典解开数量的1节的应用。
We compare two naturally arising notions of unknotting number for 2-spheres in the 4-sphere: namely, the minimal number of 1-handle stabilizations needed to obtain an unknotted surface, and the minimal number of Whitney moves required in a regular homotopy to the unknotted 2-sphere. We refer to these invariants as the stabilization number and the Casson-Whitney number of the sphere, respectively. Using both algebraic and geometric techniques, we show that the stabilization number is bounded above by one more than the Casson-Whitney number. We also provide explicit families of spheres for which these invariants are equal, as well as families for which they are distinct. Furthermore, we give additional bounds for both invariants, concrete examples of their non-additivity, and applications to classical unknotting number of 1-knots.
