2013 Fiscal Year Final Research Report
Study on Diffeomorphism Groups preserving a Geometric Structure
| Project/Area Number |
23540111
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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 Sangyo University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | 微分同相群 / 幾何構造 / 一様完全性 / 交換子長 / 擬準同型写像 / 単純性 |
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| Research Abstract |
In order to clarify geometric structures on a manifold, I studied the algebraic structure of the diffeomorphism group preserving a geometric structure. As results, I got (1) characterization of the simplicity of the leaf preserving diffeomorphism group for foliated manifolds, (2) consideration of commutator length for leaf preserving diffeomorphisms, especially characterization of the uniform perfectness of the groups for 1 dimensional foliations on the 2-torus and (3) for manifold pair (M,N), characterization of the uniform perfectness of the diffeomorphism group D(M,N) preserving N.
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Research Products
(9 results)
