论文标题
在4个manifolds中的一致性与沉浸双球
Concordance of spheres in 4-manifolds with an immersed dual sphere
论文作者
论文摘要
令$ s_0 $和$ s_1 $为两个同型，定向的2个spheres，嵌入了可定向的4个manifold $ x $中。在讨论了几项将3个manifold浸入5个manifold中的操作之后，我们讨论了自由人 - Quinn（FQ）和Stong（Stong）一致性障碍。当这些定义为$ s_0（s_1 $）时，它们将根据常规同型从$ s_0 $到$ s_1 $的自身交流集进行定义。当$ s_0 $具有沉浸式双球体时，我们会看到在$ x $的一些温和拓扑条件下，不变的FQ和Stong是一组完整的一致性障碍。这项工作是理查德·斯通（Richard Stong）的方法适应了2个spheres的一致性的背景。
Let $S_0$ and $S_1$ be two homotopic, oriented 2-spheres embedded in an orientable 4-manifold $X$. After discussing several operations for modifying an immersion of a 3-manifold into a 5-manifold, we discuss the Freedman--Quinn (fq) and Stong (stong) concordance obstructions. When these are defined for the pair $S_0,S_1$, they are defined in terms of the self-intersection set of a regular homotopy from $S_0$ to $S_1$. When $S_0$ has an immersed dual sphere, we see that under some mild topological conditions on $X$, the invariants fq and stong are a complete set of concordance obstructions. This work is an adaption of the methods of Richard Stong to the context of concordances of 2-spheres.
