Floer cohomology of Lagrangian submanifolds with non-commutative group actions
| Project/Area Number |
16K05120
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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 | Ibaraki University |
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Principal Investigator |
IRIYEH Hiroshi 茨城大学, 理工学研究科(理学野), 准教授 (30385489)
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | Floerコホモロジー / ラグランジュ部分多様体 / 旗多様体 / 対蹠集合 / 実形 / 凸体 / Mahler予想 / Hofer-Zehnder容量 / トポロジー / Floerホモロジー / 幾何学 |
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| Outline of Final Research Achievements |
We carried out concrete research for symplectic invariants, especially, Lagrangian Floer cohomology. In particular, we explicitly calculated the Lagrangian Floer cohomology of a pair of real forms even with different topological types in a complex flag manifold on which a non-commutative group acts transitively. Furthermore, we affirmatively solved the three dimensional case of Mahler's conjecture concerning the volume of convex bodies. As an application, we obtained new knowledge about the Hamiltonian dynamics on a class of six dimensional convex domains.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究課題の主題であるシンプレクティック不変量を通じて、凸幾何の分野の有名な古典的未解決問題であるMahler予想(1939年)に本質的な寄与ができた。特に、３次元の場合を解決した論文は凸幾何の分野のかなり多くの研究者の興味を喚起し、国際的な波及効果が出ている。Mahler予想は、凸幾何の中でも体積に関わる中心課題の一つであるため、今回の成果の高次元化に向かって、関連する分野の活性化が十分に期待できる。
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Report
(5 results)
Research Products
(13 results)
