论文标题
镜头空间上几乎明确的接触结构的符号填充物
Symplectic fillings of virtually overtwisted contact structures on lens spaces
论文作者
论文摘要
透镜空间上标准紧密接触结构的符号填充物已理解和分类。如果人们认为非标准的紧密结构（即实际上已列出的那些），则情况会有所不同，为此仍缺失了分类方案。在这项工作中，我们采用不同的方法并采用各种技术来提高我们对几乎经过的接触结构的符号填充的了解。我们研究表面上的曲线配置，以解决特定的晶状体空间家族的情况。然后，我们通过查看整数晶格的代数特性和固体Tori的几何切片，对任何晶状体空间的Stein填充物的拓扑拓扑构成一般限制。此外，我们试图将这些歧管放在代数几何形状的背景下，以确定是否可以将斯坦因填充物实现为Hypersurfce奇异性的Milnor纤维，从而找到一系列必要条件来实现这种情况。在论文的结论部分中，我们着重于平面联系人3-manifolds与Artin演示理论之间的联系。
Symplectic fillings of standard tight contact structures on lens spaces are understood and classified. The situation is different if one considers non-standard tight structures (i.e. those that are virtually overtwisted), for which a classification scheme is still missing. In this work we use different approaches and employ various techniques to improve our knowledge of symplectic fillings of virtually overtwisted contact structures. We study curves configurations on surfaces to solve the problem in the case of a specific family of lens spaces. Then we give general constraints on the topology of Stein fillings of any lens space by looking at algebraic properties of integer lattices and at geometric slicing of solid tori. Furthermore, we try to place these manifolds in the context of algebraic geometry, in order to determine whether Stein fillings can be realized as Milnor fibers of hypersurfce singularities, finding a series of necessary conditions for this to happen. In the concluding part of the thesis, we focus on the connections between planar contact 3-manifolds and the theory of Artin presentations.
