论文标题
固体圆环上紧密接触结构的分类
Classification of tight contact structures on a solid torus
论文作者
论文摘要
接触几何学是一个基本的问题，可以对给定的3个manifold上的所有非同位素紧密接触结构进行分类。如果歧管具有边界，我们还需要指定边界上的分隔集。在本文中，我们通过写下封闭式的公式，以完全在固体圆环边界上设置任何给定的划分，从而完全回答了固体圆环的情况。以前，由于本田的工作，只有少数特殊案例被知道。
It is a basic question in contact geometry to classify all non-isotopic tight contact structures on a given 3-manifold. If the manifold has a boundary, we need also specify the dividing set on the boundary. In this paper, we answer the classification question completely for the case of a solid torus by writing down a closed formula for the number of non-isotopic tight contact structures with any given dividing set on the boundary of the solid torus. Previously, only a few special cases were known due to work by Honda.
