论文标题
镜头空间的无构型接线图
Unbraided wiring diagrams for Stein fillings of lens spaces
论文作者
论文摘要
在先前的工作中，我们在任何配备其规范接触结构的镜头空间的河口填充的每个Stein填充上构建了平面Lefschetz振动。在这里，我们描述了一种算法，以绘制一个未编写的接线图，其相关的平面Lefschetz纤维通过Plamenevskaya和Starkston的方法获得，在该方法中，及其规范接触结构的镜头空间被视为循环镜的触点链接，与Lefschetz Fibration Atered Atered fortibe inder hydibe inder hectibe inder in.再加上Plamenevskaya和Starkston的工作，我们获得了以下结果：我们描述的接线图可以扩展到$ \ Mathbb {C c}^2 $中具有标记点的符号图形磁盘的布置，包括这些磁盘的所有交叉点，从而使这些磁盘的所有交叉点都可以通过这些片段来验证，从而可以通过这些片段来验证这些张开的范围，从而使这些变换均可换成这些盘的变换。 $ \ mathbb {c}^2 $沿着那些标记的点，一个人与lefschetz振动一起恢复了施坦的填充。此外，该布置与装饰的平面曲线胚芽有关，该曲线胚芽代表光滑的图形同型循环商奇异性。 作为另一个应用程序，我们在任何透镜空间的坦格填充物及其规范接触结构的Stein填充物与相应循环商奇异性的Milnor纤维之间建立了明确的两者，这是由Némethi和Popescu-Pampu首先获得的。
In a previous work, we constructed a planar Lefschetz fibration on each Stein filling of any lens space equipped with its canonical contact structure. Here we describe an algorithm to draw an unbraided wiring diagram whose associated planar Lefschetz fibration obtained by the method of Plamenevskaya and Starkston, where the lens space with its canonical contact structure is viewed as the contact link of a cyclic quotient singularity, is equivalent to the Lefschetz fibration we constructed on each Stein filling of the lens space at hand. Coupled with the work of Plamenevskaya and Starkston, we obtain the following result as a corollary: The wiring diagram we describe can be extended to an arrangement of symplectic graphical disks in $\mathbb{C}^2$ with marked points, including all the intersection points of these disks, so that by removing the proper transforms of these disks from the blowup of $\mathbb{C}^2$ along those marked points one recovers the Stein filling along with the Lefschetz fibration. Moreover, the arrangement is related to the decorated plane curve germ representing the cyclic quotient singularity by a smooth graphical homotopy. As another application, we set up an explicit bijection between the Stein fillings of any lens space with its canonical contact structure, and the Milnor fibers of the corresponding cyclic quotient singularity, which was first obtained by Némethi and Popescu-Pampu, using different methods.
