论文标题
两个链扭曲
Two strand twisting
论文作者
论文摘要
我们证明，对于所有$ k \ geq 2 $，无法使用$ \ bar {t} _ {2k} $移动纤维结。更一般而言，我们在两个链扭曲操作的数量上给出了上限，这些链扭曲操作可以从最小的交叉数和辫子索引来取消与非平凡的homfly多项式结的结。作为副产品，我们证明不能通过$ t_ {2k} $移动来降低两桥结的辫子索引，但对于所有\ Mathbb {n} $有限的$ k \ y move，也无法降低。
We prove that fibred knots cannot be untied with $\bar{t}_{2k}$-moves, for all $k \geq 2$. More generally, we give an upper bound on the number of two strand twist operations that allow to untie a knot with non-trivial HOMFLY polynomial, in terms of the minimal crossing number, and the braid index. As a by-product, we prove that the braid index of a two-bridge knot cannot be lowered by applying $t_{2k}$-moves, for all but finitely many $k \in \mathbb{N}$.
