2011 Fiscal Year Final Research Report
A research of the automorphism group of a free group
| Project/Area Number |
21740050
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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 | Tokyo University of Science (2011)
Kyoto University (2009-2010) |
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Principal Investigator |
SATOH Takao 東京理科大学, 理学部第二部・数学科, 講師 (70533256)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 自由群の自己同型群 / Johnson準同型 / 曲面の写像類群 |
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| Research Abstract |
Our main results of this research are as follows : (1) We determined the cokernel of the Johnson homomorphism associated to the lower central series of the IA-automorphism group of a free group. (2) We gave combinatorial descriptions of the GL-decomposition of the Johnson cokernels and the derivation algebra of the free Lie algebra. (3) We constructed new series of obstructions for the surjectivity of the Johnson homomorphism of the mapping class group of a surface. (4) We computed the first cohomology group of the automorphism group of a free group with coefficients in the abelianization of the IA-automorphism group.
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Research Products
(33 results)
