2017 Fiscal Year Final Research Report
Study on diffeomorphism groups and geometric structure on ends of noncompact manifolds
| Project/Area Number |
15K04874
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kyoto Institute of Technology |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
IKAWA Osamu 京都工芸繊維大学, 基盤科学系, 教授 (60249745)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | 微分同相群 / 一様同相群 / 非コンパクト多様体 / エンド / 距離幾何 / リーマン計量 / 双曲幾何 |
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| Outline of Final Research Achievements |
In geometry, various classes of manifolds constitute important subjects of research. The whole continuous transformations on a manifold form a group, which is called the homeomorphism group of this manifold. Study of this group plays an important role to understand the geometric nature of the manifold.
In this research we are concerned with open manifolds with metrics, as Euclidean spaces, and the groups of uniform homeomorphisms on those manifolds. A uniform homeomorphism is a transformation on a manifold which satisfies a sort of uniform estimate of continuity, called the uniform continuity, with respect to the given metric. Those groups of uniform homeomorphisms are naturally endowed with the uniform topology induced from the metrics on the manifolds. With this uniform topology we studied local and global continuous deformation of those groups and obtained a list of metric manifolds for which the groups of uniform homeomorphisms admit local or global continuous deformations.
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| Free Research Field |
位相幾何学
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