论文标题
戈迪安图在无穷大的行为
Behavior of Gordian graphs at infinity
论文作者
论文摘要
本文是指结理论，并致力于研究各种局部移动的戈尔德图的全球性质。 2005年，Gambaudo和Ghys提出了Crossing Change Gordian图的无限行为的问题。他们提出了研究其“末端”，即有界子集补充的无限连接组件。我们提供了来自Infinity的行为的完整描述，用于从三个著名的无限家庭进行本地移动，即理性的举动，$ C（n）$ - 移动和$ h（n）$ - 移动（请注意，前两个家庭中的每个家庭都包含交叉变化）。同样，在2005年，Marché对Infinity的Gordian图表的行为有了不同的看法，建议考虑有限子集的补充。我们在这种意义上描述了无穷大的行为，用于所有局部移动，并在相应的Gordian图中使用Unknot的无限邻居。
The present paper refers to the knot theory and is devoted to the study of global properties of Gordian graphs of various local moves. In 2005, Gambaudo and Ghys raised the question of the behavior at infinity of the crossing change Gordian graph. They proposed studying its "ends", that is, unbounded connected components of complements of bounded subsets. We provide a complete description of the behavior at infinity for local moves from three well-known infinite families, namely, rational moves, $C(n)$-moves, and $H(n)$-moves (note that each of the first two families contains the crossing change). Also, in 2005, Marché gave a different perspective on the behavior of Gordian graphs at infinity, proposing to consider complements of finite subsets. We describe the behavior at infinity in this sense for all local moves with the infinite neighborhood of the unknot in the corresponding Gordian graph.
