Unknotting twisted knots with Gauss diagram forbidden moves
Unknotting twisted knots with Gauss diagram forbidden moves
复制标题
用高斯图解开扭结的禁忌动作
DOI：
10.1142/s0218216523500086
复制
发表时间：
2021
影响因子：
0.5
通讯作者：
Qingying Deng
中科院分区：
文献类型：
--
作者：
Shudan Xue;Qingying Deng
扭结理论，由 M.O. 提出布尔昆，是虚拟结理论的推广。众所周知，任何虚拟结都可以通过广义 Reidemeister 步的有限序列和两个禁止步 F 1 和 F 2 变形为平凡结。类似地，我们证明任何扭曲结也可以通过扩展 Reidemeister 步的有限序列和三个禁止步 T 4、F 1 （或 F 2）和 F 3 （或 F 4）变形为平凡结或带杆的平凡结。 。
Twisted knot theory, introduced by M.O. Bourgoin, is a generalization of virtual knot theory. It is well-known that any virtual knot can be deformed into a trivial knot by a finite sequence of generalized Reidemeister moves and two forbidden moves F 1 and F 2. Similarly, we show that any twisted knot also can be deformed into a trivial knot or a trivial knot with a bar by a finite sequence of extended Reidemeister moves and three forbidden moves T 4, F 1 (or F 2) and F 3 (or F 4) .