论文标题
浸入四个空间的表面的最小生成运动集
Minimal generating sets of moves for surfaces immersed in the four-space
论文作者
论文摘要
对于四个空间中的沉浸表面，我们有一组生成的swenton - hughes- kim-miller空间移动，这些移动与这些表面的环境同位素浸入式环境同位素浸入相关联。我们还拥有Yoshikawa-Kamada-Kawauchi-Kim-李平面移动，这些移动与这些表面的环境同位素沉浸式的明显图形图相关联。人们可以询问前者是否形成最小的集合，以及后者的移动是否形成生成集。在本文中，我们得出了一个最小生成的空间移动集，用于沉浸在四空间中的表面图，这转化为一组生成的平面移动。我们还表明，可以通过不需要1-1柄或2-1柄幻灯片的柯比微积分将两个等效浸泡表面的补充彼此转换。我们还讨论了四个空间中浸泡的表面链接补体的基本组，并讨论了定向沉浸式的表面链接的不变性。
For immersed surfaces in the four-space, we have a generating set of the Swenton--Hughes--Kim--Miller spatial moves that relate singular banded diagrams of ambient isotopic immersions of those surfaces. We also have Yoshikawa--Kamada--Kawauchi--Kim--Lee planar moves that relate marked graph diagrams of ambient isotopic immersions of those surfaces. One can ask if the former moves form a minimal set and if the latter moves form a generating set. In this paper, we derive a minimal generating set of spatial moves for diagrams of surfaces immersed in the four-space, which translates into a generating set of planar moves. We also show that the complements of two equivalent immersed surfaces can be transformed one another by a Kirby calculus not requiring the 1-1-handle or 2-1-handle slides. We also discuss the fundamental group of the immersed surface-link complement in the four-space and a quandle coloring invariant of an oriented immersed surface-link.
