Study on quasipositive surfaces in manifolds with contact structures and applications to complex singularity theory

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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 on S. In this project, we studied the Milnor fibration of an isolated singularity of a polynomial map which is obtained as a product of a complex polynomial and a complex conjugate polynomial, and proved that the compatible contact structure of such a Milnor fibration is always not the standard one.