Gordian adjacency for torus knots
Gordian adjacency for torus knots
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环面结的戈尔迪邻接
DOI：
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发表时间：
2013
期刊：
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通讯作者：
P. Feller
中科院分区：
文献类型：
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作者：
P. Feller
如果存在一个包含K的解结序列，则将结点K称为结点L的Gordian邻接。通过对加厚环面中结点的研究，给出了环面结点Gordian邻接的充分条件。我们还使用Levine-Tristram签名作为Gordian邻接的障碍，完整地描述了索引2和3的环面结的Gordian邻接性。最后，将环面结点的Gordian邻接性与平面曲线奇异点的邻接性进行了比较。
A knot K is called Gordian adjacent to a knot L if there exists an unknotting sequence for L containing K. We provide a sufficient condition for Gordian adjacency of torus knots via the study of knots in the thickened torus. We also completely describe Gordian adjacency for torus knots of index 2 and 3 using Levine-Tristram signatures as obstructions to Gordian adjacency. Finally, Gordian adjacency for torus knots is compared to the notion of adjacency for plane curve singularities.