什么时候可以通过交叉交换和平滑从另一个链接中获得链接？
When can a link be obtained from another using crossing exchanges and smoothings?
摘要：
设$L$为固定链路。给定一个链路图$D$，是否有一个序列的交叉交换和平滑$D$，产生一个图的$L$？我们从计算复杂性的角度来处理这个问题。从远藤、伊藤和谷山的工作中可以得出，如果$L$是一个交叉数最多为$5$的素链路，那么有一个算法可以在多项式时间内回答这个问题。我们表明，同样适用于所有环面链接$T_{2,m}$和所有扭曲结。
英文摘要：
Let $L$ be a fixed link. Given a link diagram $D$, is there a sequence of crossing exchanges and smoothings on $D$ that yields a diagram of $L$? We approach this problem from the computational complexity point of view. It follows from work by Endo, Itoh, and Taniyama that if $L$ is a prime link with crossing number at most $5$, then there is an algorithm that answers this question in polynomial time. We show that the same holds for all torus links $T_{2,m}$ and all twist knots.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
