论文标题
关于某些表面奇点链接的符号填充的独特性
On uniqueness of symplectic fillings of links of some surface singularities
论文作者
论文摘要
我们考虑了理性表面奇点与基本周期降低的链接的规范接触结构。这些奇异性可以以其双分辨率图来表征：图是一棵树，每个顶点的重量不高于其负值。在与Starkston的联合工作中，我们先前表明，如果图中每个顶点的重量最多为-5，则接触结构具有独特的符号填充（直至符号变形和爆炸）。证明是基于对de jong-van Straten对这些奇异性平滑的描述的符合类似物。在本文中，我们通过分析支持这些接触结构的平面开放式书籍的正面单层分析，给出了简短的填充独特性证明。
We consider the canonical contact structures on links of rational surface singularities with reduced fundamental cycle. These singularities can be characterized by their dual resolution graphs: the graph is a tree, and the weight of each vertex is no greater than its negative valency. In a joint work with Starkston, we previously showed that if the weight of each vertex in the graph is at most -5, the contact structure has a unique symplectic filling (up to symplectic deformation and blow-up). The proof was based on a symplectic analog of de Jong-van Straten's description of smoothings of these singularities. In this paper, we give a short self-contained proof of uniqueness of fillings, via analysis of positive monodromy factorizations for planar open books supporting these contact structures.
