2009 Fiscal Year Final Research Report
Non commutative geometry and moduli spaces of holomorphic curves
| Project/Area Number |
18540079
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kyoto University |
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Principal Investigator |
KATO Tsuyoshi Kyoto University, 大学院・理学研究科, 教授 (20273427)
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| Project Period (FY) |
2006 – 2009
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| Keywords | キャパシティー / モジュライ理論 |
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| Research Abstract |
Mainly we have two results. One is on the construction of moduli spaces over Casson handles which are non compact smooth four manifolds. In general in order to construct moduli theory over non compact spaces, there are two steps which should be done, where one is Fredholm theory, and the other is transversality theory. For the former we have already done over the Casson handles. During this research periods, we have constructed transversality theory over the Casson handles by use of an approximation method. The other result is to construct a globally analytic relation on the set of polynomial type partial differential equations of two variables. It is given by use of a rough asympototic comparison between positive solutions to different PDEs. In particular we have verified that the relation is non trivial by analyzing the structure of the moduli space with respect to the relation.
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