2011 Fiscal Year Final Research Report
Topological studies on the surface embedded on 4-dimensional manifolds and their deformations
| Project/Area Number |
20540083
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tokyo University of Science (2011)
Saga University (2008-2010) |
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Principal Investigator |
HIROSE Susumu 東京理科大学, 理工学部, 准教授 (10264144)
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| Co-Investigator(Kenkyū-buntansha) |
MAEDA Sadahiro 佐賀大学, 大学院・工学系研究科, 教授 (40181581)
ICHIKAWA Takashi 佐賀大学, 大学院・工学系研究科, 教授 (20201923)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 位相幾何学 / 低次元トポロジー / 写像類群 / 曲面結び目 / 4次元多様体 |
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| Research Abstract |
In order to improve the study on deformations and the mapping class groups of closed surfaces embedded in 4-manifolds, we made several researches on the mapping class group from the topological viewpoint. Especially, we obtained results on the uniqueness of periodic maps with large periods, the regular homotopic deformations of the bounded surface embedded in the 3-sphere, the Nielsen realization problems on the mapping class groups of the 3-dimensional handlebodies, and the mapping class groups of the nonorientable closed surfaces standardly embedded in the 4-sphere.
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