2009 Fiscal Year Final Research Report
Research on open book decompositions appearing on the boundary of complex domains with contact structures
| Project/Area Number |
19740029
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Tohoku University (2008-2009)
Tokyo Institute of Technology (2007) |
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Principal Investigator |
ISHIKAWA Masaharu Tohoku University, 大学院・理学研究科, 准教授 (10361784)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 特異点論 / 接触構造 / 3次元多様体論 / 結び目理論 |
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| Research Abstract |
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.
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