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

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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.