Research of 3-manifolds by topological and hyperbolic geometric method
| Project/Area Number |
18540097
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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 Tokyo Metropolitan University, 大学院・理工学研究科, 教授 (50154688)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥600,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | 位相幾何学 / 微分トポロジー / hyperbolic 3-manifolds / Ending Lamination Con jecture / curve complex / geometric limits / Seifert fibered space / Kleinian groups / 3次元多様体 / 双曲幾何学 / クライン群 / 曲線複体 / 双曲多様体 / エンディング・ラミネーション / ending lamination / quasi-Fuchsian groups / Marden's conjecture / ruled wrappings / Seifert fibered spaces / Lozi maps / shadowing property |
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| Research Abstract |
I introduced the notion of ruled wrappings and by using it gave a simple alternative proof of Marden's conjecture. We completed the geometric classification of geometric limits hyperbolic manifolds which are given by geometric limits of sequences of hyperbolic 3-manifolds with fundamental groups isometric to compact surface groups. In particular, we proved that, if these two geometric manifolds are homeomorphic and have the same end invariants, the homeomorphism is properly homotopic to an isometry.
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Report
(6 results)
Research Products
(30 results)
