The focused study of automorphism groups of free groups and the mapping class groups for the Johnson homomorphisms
| Project/Area Number |
24740051
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
Satoh Takao 東京理科大学, 理学部, 准教授 (70533256)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 自由群の自己同型群 / Johnson準同型 / 群のコホモロジー / 写像類群 / SL_2 Fricke指標環 / SL_2普遍指標環 / Fricke指標 / IA自己同型群 / 曲面の写像類群 / Torelli群 |
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| Outline of Final Research Achievements |
We obtained many new results for the Andreadakis-Johnson filtration and the Johnson homomorphisms of the automrophism groups of free groups. In particular, we gave the affirmative answer to the Andreadakis conjecture for the upper triangular automorphism groups, and established an analogue of the Johnson-Morita theory by using the rings of Fricke characters of free groups and the rings of SL(m,C)-representations of free groups. We expect that these results have good applications for the study of the mapping class groups of surfaces.
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Report
(5 results)
Research Products
(25 results)
