翻转桥曲面与稳定桥数的界
Flipping bridge surfaces and bounds on the stable bridge number
摘要：
我们证明了，如果$K$是一个结在$S^3$和$Σ$是一个桥梁领域的$K$与高距离和$2n$穿刺，所需的扰动数的$K$交换的两个球有界的$Σ$通过一个合痕是$n$。我们还构造了一个具有两个不同桥球的纽结，分别具有$2n$和$2n-1$桥，其中任何共同的扰动至少具有$3n-1$桥。我们将这两个结果推广到任何3流形中的节点的桥接曲面。
英文摘要：
We show that if $K$ is a knot in $S^3$ and $Σ$ is a bridge sphere for $K$ with high distance and $2n$ punctures, the number of perturbations of $K$ required to interchange the two balls bounded by $Σ$ via an isotopy is $n$. We also construct a knot with two different bridge spheres with $2n$ and $2n-1$ bridges respectively for which any common perturbation has at least $3n-1$ bridges. We generalize both of these results to bridge surfaces for knots in any 3-manifold.
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。
