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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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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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 / 向き付け不可能閉曲面 / 2次元結び目 / 3次元ハンドル体 / リーマン面 / 無限離散群 / 周期的写像 / 零同境写像 / 擬アノソフ同相写像 / 正則ホモトピー / 埋め込み |
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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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Report
(6 results)
Research Products
(49 results)
