| Project/Area Number |
22540092
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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 | Tokyo Metropolitan University |
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Principal Investigator |
SOMA Teruhiko 首都大学東京, 理工学研究科, 教授 (50154688)
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| Co-Investigator(Kenkyū-buntansha) |
OHSHIKA Ken'ichi 大阪大学, 大学院理学研究科, 教授 (70183225)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 位相幾何学 / 微分トポロジー / クライン群 / 双曲幾何学 / 幾何構造 / Smale 予想 / 微分同相群 / 双曲多様体 / 幾何的極限 / スメール予想 / エノン写像 / ヘテロ次元接触 / 代数的極限 / 曲線複体 / ストレンジ・アトラクタ / Smale予想 / Seifert多様体 / 3次元多様体 / 微分同相写像 / Henon写像 |
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| Research Abstract |
The aim of this research is to prove fundamental theorems to explain uniformly main results on topological Kleinian group theory. In particular, we are interested in the topological and geometrical classifications of geometric limits of Kleinian groups. Before our research, this classification was done only for sequences of special Kleinian groups (e.g. quasi-Fuchsian groups) which admit algebraic limits. Though this project, we have succeeded in classifying topologically and geometrically geometric limits of an sequences of geometrically finite Kleinian groups which have the same topological type which do not necessarily converge algebraically. Moreover, as an application, we have proved that the Ending Lamination Theorem for geometric limits.
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