Study of the geography for 4-dimensional topology and of surgery via mapping class groups
| Project/Area Number |
16K17601
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Okayama University (2017-2020)
Osaka Electro-Communication University (2016) |
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Principal Investigator |
Monden Naoyuki 岡山大学, 自然科学研究科, 准教授 (60611986)
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | Lefschetz fibration / 写像類群 / 線織面 / 有限表示群 / 既約性 / 曲面上の曲面束 / 安定交換子長 / 4次元シンプレクティック多様体 / 地誌学 / トポロジー / 幾何学 |
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| Outline of Final Research Achievements |
In 4-dimensional topology, fiber bundle structures and fiber space structures of 4-manifold are important objects of research. We constructed some new examples of Lefschetz fibrations and surface bundles over surfaces. In addition, we gave a new upper bound for stable commutator length of a Dehn twist in the mapping class group of a surface.
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| Academic Significance and Societal Importance of the Research Achievements |
4次元を境にトポロジーの研究は大きく変わる. 他の次元に比べて4次元多様体の全体像はわかっていない部分が多いため, 様々な例を構成することにより全体像の振る舞いを調べようという研究が活発に行われている. 本研究は新たな4次元多様体を構成したり, 4次元多様体に入るLefschetz fibrationや曲面上の曲面束の構造の新たな例を構成したことにより, 4次元多様体の全体像の解明への足掛かりになるものと思われる.
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Report
(6 results)
Research Products
(7 results)
