2015 Fiscal Year Final Research Report
Research on the intersection of a pair of homogeneous Lagrangian submanifolds and Floer homology
| Project/Area Number |
24740049
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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 | Ibaraki University (2015)
Tokyo Denki University (2012-2014) |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | Floerコホモロジー / ラグランジュ部分多様体 / 複素旗多様体 / 実形 / 対蹠集合 / ハミルトン体積最小性 |
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| Outline of Final Research Achievements |
The purpose of this research is to reveal the symplectic topological nature of
a Lagrangian submanifold with a high degree of symmetry in a symplectic manifold. There were few concrete studies concerned with this kind of Lagrangian submanifold. By using the symmetries of these spaces, in particular in the complex projective space, we obtained the results about homological rigidity of Lagrangian submanifolds, explicit calculations of Lagrangian Floer cohomology, including an application to the Hamiltonian volume minimizing problem.
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| Free Research Field |
数物系科学
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