论文标题
分数Dehn Twist系数的切片 - 苯甲刚不等式
The slice-Bennequin inequality for the fractional Dehn twist coefficient
论文作者
论文摘要
我们将$ n $ stranded辫子组的分数Dehn Twist系数（FDTC）描述为独特的均质准它形成的绝对数字，最多等于1等于$（N-1）$（N-1）$ - 固定编织的编织子系统的缺陷1等于1。在不同的方向上，我们确定斜杆不平等与FDTC代替了writhe。换句话说，我们根据编织的FDTC建立了一个蛋白质封闭的光滑切片属的仿射线性下限。我们还讨论了这两个看似无关的结果之间的联系。在附录中，我们为Slice-Bennequin不平等及其FDTC提供了一个统一的框架。
We characterize the fractional Dehn twist coefficient (FDTC) on the $n$-stranded braid group as the unique homogeneous quasimorphism to the real numbers of defect at most 1 that equals 1 on the positive full twist and vanishes on the $(n-1)$-stranded braid subgroup. In a different direction, we establish that the slice-Bennequin inequality holds with the FDTC in place of the writhe. In other words, we establish an affine linear lower bound for the smooth slice genus of the closure of a braid in terms of the braid's FDTC. We also discuss connections between these two seemingly unrelated results. In the appendix we provide a unifying framework for the slice-Bennequin inequality and its counterpart for the FDTC.
