论文标题
焊接结的无结
An unknotting invariant for welded knots
论文作者
论文摘要
我们研究了焊接结上的局部转换，这是虚拟结上虚拟化移动的类似物。由于这一举动是一个毫无打结的操作，因此我们为焊接结定义了一个不变的扭曲数字。我们将无调的扭曲数与翘曲度和焊接的无结数字联系起来，并使用Alexander Quandle着色在扭曲数字上建立一个下限。我们还通过Twist Move研究了焊接结之间的Gordian距离，并定义了相应的Gordian复合体。
We study a local twist move on welded knots that is an analog of the virtualization move on virtual knots. Since this move is an unknotting operation we define an invariant, unknotting twist number, for welded knots. We relate the unknotting twist number with warping degree and welded unknotting number, and establish a lower bound on the twist number using Alexander quandle coloring. We also study the Gordian distance between welded knots by twist move and define the corresponding Gordian complex.
