论文标题
镜头空间符号填充的合理排列图
Rational blowdown graphs for symplectic fillings of lens spaces
论文作者
论文摘要
在先前的工作中，我们证明了所有定向镜头空间的每种最小符合性填充，被视为某些环状商奇异性的奇异性链接并配备了其规范接触结构，可以通过沿线性阳性图的一系列奇异序列来获得奇异性的最小分辨率。在这里，我们从凸多边形的三角剖分方面给出了更简单的视觉呈现。结果，我们能够组织所有具有其规范接触结构的给定晶状体空间的所有最小符号填充物的符号变形等效类别，作为分级，有向，扎根和连接的图形，该图是根是对应的环状式镜头的最小分辨率，每个均可构图均具有符号效果。此外，我们为每个最小符号填充的合理排列深度提供了上限。
In a previous work, we proved that each minimal symplectic filling of any oriented lens space, viewed as the singularity link of some cyclic quotient singularity and equipped with its canonical contact structure, can be obtained from the minimal resolution of the singularity by a sequence of symplectic rational blowdowns along linear plumbing graphs. Here we give a dramatically simpler visual presentation of our rational blowdown algorithm in terms of the triangulations of a convex polygon. As a consequence, we are able to organize the symplectic deformation equivalence classes of all minimal symplectic fillings of any given lens space equipped with its canonical contact structure, as a graded, directed, rooted, and connected graph, where the root is the minimal resolution of the corresponding cyclic quotient singularity and each directed edge is a symplectic rational blowdown along an explicit linear plumbing graph. Moreover, we provide an upper bound for the rational blowdown depth of each minimal symplectic filling.
