2013 Fiscal Year Final Research Report
Structure of mapping class groups and topology of 4-manifolds
| 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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| 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 |
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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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