透镜空间手术治疗A'Campo分裂结

Milnor fibration, A'Campo's divide and Turaev's shadow

We give a method for constructing a shadowed polyhedron from a divide. The 4-manifold reconstructed from a shadowed polyhedron admits the structure of a Lefschetz fibration if it satisfies a certain property, which we call the LF-property. We will show that the shadowed polyhedron constructed from a divide satisfies this property and the Lefschetz fibration of this polyhedron is isomorphic to the Lefschetz fibration of the divide. Furthermore, applying the same technique to certain free divides we will show that the links of those free divides are fibered with positive monodromy.

分隔链路示意图

Diagrams of divide links

最近，N.A 'Campo提出了一个链接的构建，从一个通用的曲线浸入到一个2-磁盘中。它与奇点理论密切相关。在本文中，我们给出了一个简单的程序来绘制一个图表的链接从图片的曲线。

Berge透镜空间散在结节的分结表现

Divide knot presentation of sporadic knots of Berge's lens space surgery

分割结点和链环是由A'Campo在复曲线的奇异性理论中定义的一种用实平面曲线表示结点或链环的方法。本文是作者以前结果的继续，即Berge的透镜空间手术的主要亚族中的每个结（即，通过Dehn手术产生透镜空间的结）由L形曲线表示为分割结。在本文中，L形曲线的推广，它表明，每一个小的子家庭，称为零星的例子，Berge的透镜空间手术的结是由一个广义的L形曲线作为一个分割结。本文还归纳了手术系数的计算公式和表示方法。

Divides with cusps and Kirby diagrams for line arrangements

The complement of a complexified real line arrangement is an affine surface. It is classically known that such a space has a handle decomposition up to $2$-handles. We will describe the handle decomposition induced from Lefschetz hyperplane section theorem for such a space. To describe the Kirby diagram, we introduce the notion of the divide with cusps which is a generalization of the divide introduced by A'Campo.

通过迹映射实现实形变

Real morsifications via the trace map

该研究证明所有既约实平面曲线奇点都存在实形变，通过提出迹映射方法，克服非实分支共轭对的障碍，解决了相关长期问题。

（-2，3，n）椒盐卷饼结的Culler-Shalen范数

The Culler-Shalen seminorms of the (-2,3,n) pretzel knot

证明了当3不整除n（3整除n）时，（-2，3，n）椒盐卷饼结的SL（2，C）-特征簇由两条（分别为三条）代数曲线组成，并给出了这些曲线的Culler-Shalen范数的显式计算.利用这个计算，我们描述了基本多边形和牛顿多边形的这些节点，并给出了一个列表的Dehn手术产生的流形有限或循环的基本群。这构成了这些纽结的性质P的新证明。