2011 Fiscal Year Final Research Report
Automorphism group of a smooth G-manifold and its applications.
| Project/Area Number |
21540074
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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 | Shinshu University |
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Principal Investigator |
ABE Kojun 信州大学, 理学部, 特任教授 (30021231)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 微分同相群 / 群の完全性 / 1次元ホモロジー群 / 可微分G-多様体 / 一様完全性 / 同変微分同相群 / 可微分軌道体 |
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| Research Abstract |
(1) Let M be a smooth G-manifold. We consider the diffeomorphisms, Lipschtz homeomorphisms and homeomorphisms of M preserving the G-action which are isotopic to the identity through the isotopies with compact support. We determined the first homology of those groups when M has codimension one orbits. From those results we see that the first homology reflects the properties of those categories.
(2) We consider the perfectness and uniformly perfectness for the group of the identity component of the diffeomorphisms of a smooth manifold pair. We have determined the condition for the group to be uniformly perfect when the dimension of the submanifold is one. The result can be applied to the knot theory.
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