论文标题
理性的纠缠替换和结浮子同源性
Rational tangle replacements and knot Floer homology
论文作者
论文摘要
从链接$ k $的链接浮子综合体中，我们提取了$ k $的理性解开数量的下限$ t_q'（k）$（即解开$ k $所需的最小理性替换次数）。此外，我们表明扭转阻塞$ t_q（k）= \ hat {t}（k）$ from Alishahi的论文，作者是适当的理性解开数字的下限。此外，$ t_q（k \ #k'）= \ max \ {t_q（k），t_q（k'）\} $和$ t'_q（k \ #k'）= \ max \ max \ {t'_q（k），t'_q（k'q（k''）\} $。对于圆环结$ k = t_ {p，pk+1} $我们计算$ t'_q（k）= \ lfloor p/2 \ rfloor $和$ t_q（k）= p-1 $。
From the link Floer complex of a link $K$, we extract a lower bound $t_q'(K)$ for the rational unknotting number of $K$ (i.e. the minimum number of rational replacements required to unknot $K$). Moreover, we show that the torsion obstruction $t_q(K)=\hat{t}(K)$ from an earlier paper of Alishahi and the author is a lower bound for the proper rational unknotting number. Moreover, $t_q(K\#K')=\max\{t_q(K),t_q(K')\}$ and $t'_q(K\#K')=\max\{t'_q(K),t'_q(K')\}$. For the torus knot $K=T_{p,pk+1}$ we compute $t'_q(K)=\lfloor p/2\rfloor$ and $t_q(K)=p-1$.
