2012 Fiscal Year Final Research Report
Diffeomorphism group of the circle and discontinuous groups of theuniversal Teichmuller curve
| Project/Area Number |
22740034
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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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 |
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| Project Period (FY) |
2010 – 2012
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| Keywords | 円周 / 微分同相群 / フックス群 / 回転数 / 収束群作用 / 相対的双曲群 / C*群環 / Cannon-Thurston写像 |
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| Research Abstract |
We studied a boundary of the smooth universal Teichmuller curve and the action of subgroups of diffeomorphism group of the circle on this boundary. Among actions of free product of two finite groups on the circle, we characterized Fuchsian actions in terms of rotation number.We obtained a result about simplicity of the reduced group C*-algebra of a group admitting convergence actions. We gave a necessary and sufficient condition for two geometrically finite convergence actions to admit an equivariant continuous map and applied it to construct examples of convergence actions.
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