2012 Fiscal Year Final Research Report
Study of groups of measure-preserving homeomorphisms and volume-preserving diffeomorphisms of noncompact manifolds
| Project/Area Number |
22540081
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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 Institute of Technology |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
HUKUI Kazuhiro 京都産業大学, 理学部, 教授 (30065883)
KOYAMA Akira 早稲田大, 理工学術院, 教授 (40116158)
KATO Hisao 筑波大学, 数理物質科学研究科, 教授 (70152733)
SAKAI Katsuro 筑波大学, 数理物質科学研究科, 准教授 (50036084)
OKURA Hiroyuki 京都工芸繊維大学, 工芸科学研究科, 教授 (80135649)
CHINEN Naotsugu 防衛大学校, 数学教育室, 教授 (20370067)
HOSAKA Tetsuya 静岡大学, 理学部, 准教授 (50344908)
MINE Kotaro 東京大学, 数理科学研究科, 特任研究員 (90512525)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 幾何学 / トポロジー / 微分同相群 / 無限次元多様体 |
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| Research Abstract |
We studied topological properties of groups of diffeomorphisms and homeomorphisms of any on-compact manifold M. Under the compact-open C∞topology, we extended a parametrized version of Moser’s theorem for volume forms to the non-compact case. As for the Whitney C∞ topology, we howed That the pair of the group of diffeomorphisms of M and the subgroup of those with compact support is Locally homeomorphic to the pair of countable box product and small box product of l2.As for the uniform topology, we also obtained some deformation theorems for spaces of uniform embeddings and Groups of uniform homeomorphisms.
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