2011 Fiscal Year Final Research Report
Research on intersection of a pair of Lagrangian submanifolds via Floer theory
| Project/Area Number |
22740043
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Tokyo Denki University |
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Principal Investigator |
IRIYEH Hiroshi 東京電機大学, 未来科学部, 准教授 (30385489)
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| Project Period (FY) |
2010 – 2011
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| Keywords | シンプレクティック多様体 / Floerホモロジー / エルミート対称空間 / 実形 / ラグランジュ部分多様体 / ハミルトン体積最小性 / Arnold-Givental不等式 / 対蹠集合 |
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| Research Abstract |
The Arnold-Givental conjecture states that the intersection number of Lagrangian submanifold L, which is the fixed point set of an anti-symplectic involution of a symplectic manifold M, and its imageΦ(L) by Hamiltonian diffeomorphismΦof M is greater than or equal to the sum of Z_2-Betti numbers of L. We tried to extend the conjecture to the case of a pair of Lagrangian submanifolds. As a result, we could formulate the generalized Arnold-Givental conjecture and prove it for the case of an irreducible Hermitian symmetric space M of compact type.
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