2016 Fiscal Year Final Research Report
Combinatorial models of character varieties and the dynamics of group actions there
| Project/Area Number |
25610010
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | 指標多様体 / Klein群 / 力学系 / Cannon-Thurston写像 |
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| Outline of Final Research Achievements |
We have obtained the following results concerning character varieties of free groups. We have accomplished the proof of the general convergence theorem for Schottky spaces, which plays a key role for understanding the topology of Schottky spaces. We have also determined the intersection of the boundaries of Schottky spaces and the space of primitive stable representations, and showed that every point there is an accumulation point of representations corresponding to closed 3-manifolds. For general Kleinian groups, we have succeeded in giving a new way of understanding Sullivan's rigidity theorem in terms of Cannon-Thurston maps. Furthermore, we have studied the relationship between non-injective points of Cannon-Thurston maps and conical limit points for general Gromov hyperbolic groups acting as convergence groups. We have published all of these results in academic journals.
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| Free Research Field |
位相幾何学
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