论文标题
关于II型链接的链接移动
On Type II Reidemeister moves of links
论文作者
论文摘要
Östlund（2001）表明，在尖端移动和三重点移动下以及有限的程度（以自距离移动中），所有平面平面曲线的平面同位素不变性是不变的。在这里，“有限程度”一词是指阿诺德·瓦西里耶夫（Arnold-Vassiliev）类型。它暗示了这种猜想，通常称为Östlund猜想：“ I型和III型雷迪德式移动足以描述从圆圈到平原到圆圈标准嵌入的任何通用沉浸式的同质性的同拷贝”。尽管如今已知反例，但没有（简单的计算）函数可以检测到平原上的反例和标准嵌入之间的差异。但是，我们引入了针对两部分情况的所需函数（高斯图公式）。
Östlund (2001) showed that all planar isotopy invariants of generic plane curves that are unchanged under cusp moves and triple point moves, and of finite degree (in self-tangency moves) are trivial. Here the term "of finite degree" means Arnold-Vassiliev type. It implies the conjecture, which was often called Östlund conjecture: "Types I and III Reidemeister moves are sufficient to describe a homotopy from any generic immersion from the circle into the plain to the standard embedding of the circle". Although counterexamples are known nowadays, there had been no (easy computable) function that detects the difference between the counterexample and the standard embedding on the plain. However, we introduce a desired function (Gauss diagram formula) is found for the two-component case.
