2009 Fiscal Year Final Research Report
Study of holomorphic foliations and vector fields
| Project/Area Number |
19684001
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | The University of Tokyo |
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Principal Investigator |
ASUKE Taro The University of Tokyo, 大学院・数理科学研究科, 准教授 (30294515)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 葉層構造 / Bott類 / Godbillon-Vey類 / Fatou集合 / Julia集合 |
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| Research Abstract |
I studied the Godbillon-Vey class of transversely holomorphic foliations, and showed that it is rigid under continuous deformations in the category of transversely holomorphic foliations. It is also shown that an invariant of deformations of foliations is closely related to the rigidity. I also introduced a new, simple definition of Fatou and Julia sets of transversely holomorphic foliations. A classification of Fatou components and some fundamental properties concerning invariant metics and conformal measures are obtained.
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