2010 Fiscal Year Final Research Report
Research on Floer theory of singular Lagrangian submanifolds
| Project/Area Number |
19740040
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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 Metropolitan University |
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Principal Investigator |
AKAHO Manabu Tokyo Metropolitan University, 理工学研究科, 助教 (30332935)
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| Project Period (FY) |
2007 – 2010
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| Keywords | シンプレクティック多様体 / フレアーホモロジー / 擬正則曲線 / ラグランジュ部分多様体 |
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| Research Abstract |
In this grant, the research worker studied Floer theory for singular Lagrangian submanifolds. In particular, he considered the following two cases ; first, immersed Lagrangian submanifolds, and secondly, Lagrangian submanifolds with Legendrian end in a symplectic manifold with concave end. For the first case, he obtained A-infinity algebras of immersed Lagrangian submanifolds with transverse double singularities, which is a joint work with D. Joyce. Secondly, he constructed Floer homology for two Lagrangian submanifolds with Legendrian end, under no bubble assumption. Moreover, he studied Morse homotopy for manifolds with boundary and obtain the definition of cup products, which tells us the direction towards A-infinity algebras of Lagrangian submanifolds with Legendrian end.
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