1998 Fiscal Year Final Research Report Summary
RIGIDITY OF GROUP ACTIONS
| Project/Area Number |
09640128
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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 | Nagoya University (1998)
Keio University (1997) |
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Principal Investigator |
KANAI Masahiko Nagoya Univ., Grad.School of Math., Professor, 大学院・多元数理科学研究科, 教授 (70183035)
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| Co-Investigator(Kenkyū-buntansha) |
MAEDA Yoshiaki Keio Univ.Dept.of Math., Professor, 理工学部, 教授 (40101076)
TONEGAWA Yoshihiro Keio Univ.Dept.of Math., Instructor, 理工学部, 助手 (80296748)
TAMURA Yozo Keio Univ.Dept.of Math., Associate Professor, 理工学部, 助教授 (50171905)
SUZUKI Yuki Keio Univ.Dept.of Math., Instructor, 理工学部, 助手 (30286645)
ITO Yuji Keio Univ.Dept.of Math., Professor, 理工学部, 教授 (90112987)
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| Project Period (FY) |
1997 – 1998
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| Keywords | rigidity of group actions / global analysis on foliated manifolds |
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| Research Abstract |
A smooth action of a discrete group GAMMA on a differentiable manifold M is, by definition, a homomorphism of GAMMA into Diff M, the diffeomorphism group of M.One of the main theme in the theory of group actions is to depict the whole space A (GAMMA, Diff M) of smooth actions of GAMMA on M.By rigidity (in a wide sense) is meant a claim which says that the space A(GAMMA, Diff M) is "small".
Invariant Geometric Structures. One of the approaches to the rigidity problem is frying to find a geometric structure that is invariant under a given group action. We found a new example for which this approach works.
Global Analysis on Foliated Manifolds. Rigidity for group actions often amounts to some global-analytic problem on a foliated manifold. We were able to describe the spectrum of the tangential laplacian on a certain foliated manifold.
Infinite-Dimensional Homogeneous Spaces of Diffeomorphism Groups. We studied geometry and topology of such spaces especially bearing an application to rigidity problem in mind.
Also there have been done researches on infinite-dimensional minimal submanifolds in infinite-dimensional spaces (by Maeda) , on the blow-up phenomenon of the Yang-Mills gradient flow (by Maeda) , on hydrodynamic limit of a spin system (by Suzuki) , and on a regularity theorem for a certain free boundary problem (by Tonegawa).
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