Research on open book decompositions appearing on the boundary of complex domains with contact structures

设S是二维复向量空间中的单位球面。对于S中的每个点x，设H是S在x处的切线空间，然后用复符号J乘法旋转H，得到另一个平面JH。H和JH的交集是切空间H中的一个2-平面。对S中的所有x都有这样一个H的集合称为S中的标准接触结构。在这个项目中，我们用S中的有边界的曲面来刻画这种接触结构，称为拟正曲面。作为这种刻画的一个例子，我们还观察到一类实解析奇点。

Let S be the unit sphere in the 2-dimensional complex vector space. For each point x in S, let H be the tangent space of S at x. We then rotate H by multiplying the complex symbol J and obtain another plane JH. The intersection of H and JH is a 2-plane in the tangent space H. The collection of such an H for all x in S is called the standard contact structure in S. In this project, we gave a characterization of this contact structure using surfaces in S with boundary, called quasipositive surfaces. We also observed a class of real analytic singularities as an example of this characterization.