| Project/Area Number |
25400082
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
Endo Hisaaki 東京工業大学, 理学院, 教授 (20323777)
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| Co-Investigator(Kenkyū-buntansha) |
菊池 和徳 大阪大学, 理学研究科, 講師 (40252572)
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| Research Collaborator |
HAYANO Kenta
YUASA Wataru
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | ４次元多様体 / 写像類群 / Lefschetzファイバー空間 / モノドロミー / ファイバー和 / 安定化 / 一般チャート理論 / 超楕円性 / 4次元多様体 / チャート表示 / 曲面結び目 / Morse-Novikov数 / 符号数 |
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| Outline of Final Research Achievements |
We studied the topology of 4-dimensional manifolds, in particular, that of Lefschetz fibrations on 4-dimensional manifolds in this research project. A Lefschetz fibration is a family of (possibly singular) surfaces parametrized by a surface and it is often studied by using the mapping class group of the fiber surface from combinatorial points of view. In this project we made use of finite graphs on surfaces to prove two stabilization theorems on Lefschetz fibrations.
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