| Project/Area Number |
21540079
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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 Institute of Technology (2011-2013)
Osaka University (2009-2010) |
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Principal Investigator |
ENDO Hisaaki 東京工業大学, 理工学研究科, 教授 (20323777)
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| Co-Investigator(Kenkyū-buntansha) |
KIKUCHI Kazunori 大阪大学, 大学院理学研究科, 講師 (40252572)
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| Project Period (FY) |
2009-04-01 – 2013-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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)
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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 / 有理ブローダウン / 微分構造 / ファイバー和 / チャート表示 / 4次元多様体 / 超楕円性 / 安定化 / トポロジー / 幾何学 / BLF / 国際情報交換 / アメリカ / 群の表示 / quandle / コサイクル |
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| Research Abstract |
It is often more difficult to examine low dimensional manifolds (3-manifolds and 4-manifolds) than to examine higher dimensional manifolds in topology. We studied the topology of 4-manifolds in this research project. In particular, we investigated Lefschetz fibrations, which are 4-manifolds consisting of infinitely many (possibly singular) surfaces (2-manifolds). We make use of mapping class groups of surfaces, which are algebraic objects related with surfaces, to describe Lefschetz fibrations. We found several close relations between some data in mapping class groups and smooth structures on total spaces of Lefschetz fibrations in this research.
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