| Project/Area Number |
18K03299
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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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| Review Section |
Basic Section 11020:Geometry-related
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| Research Institution | Osaka University |
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Principal Investigator |
Kin Eiko 大阪大学, 全学教育推進機構, 教授 (80378554)
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 写像類群 / 擬アノソフ / 組ひも群 / エントロピー / 曲線グラフ / 漸近的移動距離 / リサージュ曲線 / 位相的エントロピー / ３次元双曲多様体 / へガード分解 / ３次元多様体 / 結び目理論 / 曲線複体 / 双曲体積 / 三次元双曲多様体 / ファイバー |
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| Outline of Final Research Achievements |
We studied two invariants of pseudo-Anosov elements in the mapping class group. One is the entropy which is the translation length of the pseudo-Anosov element on the Teichmuller space. The other is the asymptotic translation length of the pseudo-Anosov element on the curve complex. (1) We gave a new construction of pseudo-Anosov braids with small normalized entropies. As an application, we determine asymptotic behaviors of minimal entropies of pseudo-Anosov elements in several subgroups (or several subsets) of mapping class groups. (Joint with Hirose, and Hirose Iguchi, Koda)(2) Given a fibered 3-manifold together with the fibered face, we give a general upper bound of asymptotic translation lengths of pseudo-Anosov monodromies associated with the fibered classes in the fibered cone.
(Joint with Baik, Shin and Wu)
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| Academic Significance and Societal Importance of the Research Achievements |
曲面の写像類群の大部分は擬アノソフ写像類である. 擬アノソフ写像類の研究は力学系理論, ３次元多様体論, 双曲幾何学などのいくつかの分野と密接に関連する. 擬アノソフ写像類の代表的な不変量(エントロピー, 漸近的移動距離, 写像トーラスの体積)とこれらの不変量の関係の研究は位相幾何学(特に写像類群の研究)において基本的なテーマであり, それ故に学術的意義がある.
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