Dynamics on curve complexes and asymptotic structure of mapping class groups
| Project/Area Number |
22654008
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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 | Osaka University |
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Principal Investigator |
OHSHIKA Kenichi 大阪大学, 大学院・理学研究科, 教授 (70183225)
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| Co-Investigator(Kenkyū-buntansha) |
SUMI Hiroki 大阪大学, 大学院・理学研究科, 准教授 (40313324)
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| Co-Investigator(Renkei-kenkyūsha) |
KIN Eiko 大阪大学, 大学院・理学研究科, 准教授 (80378554)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥3,080,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | 曲線複体 / 写像類群 / 漸近幾何 / 変形空間 / 指標多様体 / 漸近構造 / 自己同型群 / primitive sability / unmeasured lamination / dynamics / semi-group / タイヒミュラー空間 / 力学系 |
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| Research Abstract |
We studied various geometric objects, like deformation spaces of Kleinian groups, character varieties and subgroups of mapping class groups preserving Heegaard splittings and bridge decomposition, in particular their global structures, using curve complexes and their actions of mappingclass groups. We also constructed non-Hausdorff compactifications of Teichmuller spaces, and using the mapping class group actions on curve complexes, showed that their symmetry groups coincide with the extended mapping class groups.
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Report
(4 results)
Research Products
(46 results)
