2010 Fiscal Year Final Research Report
Pseudo-holomorphic map and Floer cohomology and their applications to symplectic geometry
| Project/Area Number |
19340017
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Nagoya University |
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Principal Investigator |
OHTA Hiroshi Nagoya University, 多元数理科学研究科, 教授 (50223839)
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| Co-Investigator(Kenkyū-buntansha) |
KANNO Hiroaki 名古屋大学, 多元数理科学研究科, 教授 (90211870)
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| Co-Investigator(Renkei-kenkyūsha) |
FUKAYA Kenji 京都大学, 大学院・理学研究科, 教授 (30165261)
ONO Kaoru 北海道大学, 大学院・理学研究科, 教授 (20204232)
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| Project Period (FY) |
2007 – 2010
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| Keywords | シンプレクティック幾何 / フレアーコホモロジー / ミラー対称性予想 / 擬準同型写像 / ハミルトン微分同相群 / トーリック多様体 / ポテンシャル関数 / 量子コホモロジー |
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| Research Abstract |
It is known that Lagrangian Floer cohomology can not be defined for general Lagrangian submanifolds, because of presence of bubbling off phenomena of holomorphic maps from 2-disc. We constructed a certain homotopy algebra, so called a filtered A infty algebra, associated to each Lagrangian submanifold by using holomorphic maps from 2-disc, and established the obstruction theory and deformation theory based on the algebra. We applied our general theory to the case of toric manifolds and obtained many concrete new results in symplectic geometry.
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