2013 Fiscal Year Final Research Report
Uniform research of topological Kleinian groups by using geometric limits
| 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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| Keywords | 位相幾何学 / 微分トポロジー |
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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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