2011 Fiscal Year Final Research Report
Geometric study on infinite simple groups
| Project/Area Number |
21654009
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | The University of Tokyo |
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Principal Investigator |
TSUBOI Takashi 東京大学, 大学院・数理科学研究科, 教授 (40114566)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 無限単純群 / 微分同相群 / 完全群 / 幾何学的群論 / 幾何学 / トポロジー / 代数学 |
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| Research Abstract |
We studied infinite simple groups as geometric objects where they have verious quasimorphisms and the distance function d on the set of unions of a conjugate class and its inverse. We determined the quasi isometry type with respect to the distance d of the infinite alternative group A_infty. We showed and published the result that the identity component of the group of real analytic diffeomorphisms of a manifold with good circle actions is perfect. We showed and published the result that the identity component of the group of diffeomorphisms of a closed connected manifold of dimensions not eaual to 2 and 4 is uniformly perfect and uniformly simple. We also studied the homeomorphism groups of commutator width one.
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Research Products
(7 results)
