Applications of homotopy algebras to geometry and its deformation problems
Project/Area Number |
19740038
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Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Single-year Grants |
Research Field |
Geometry
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Research Institution | Chiba University (2008-2009) Kyoto University (2007) |
Principal Investigator |
KAJIURA Hiroshige Chiba University, 大学院・理学研究科, 准教授 (30447891)
|
Project Period (FY) |
2007 – 2009
|
Project Status |
Completed (Fiscal Year 2009)
|
Budget Amount *help |
¥3,700,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥600,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,100,000 (Direct Cost: ¥1,100,000)
|
Keywords | 幾何学 / トポロジー / 代数学 / 数理物理 / 素粒子論 / ホモトピー代数 / 位相的弦理論 / Dブレイン / 三角圏 / 複素構造 |
Research Abstract |
We studied Fukaya categories which are categories consisting of Lagrangian submanifolds in symplectic manifolds. We constructed an A-infinity structure in the Fukaya category of lines in a plane completely and explicitly. Also, we studies relations between A-infinity categories and triangulated categories which are general tools to describe geometry. We constructed an example of triangulated categories whose A-infinity enhancements are not unique.
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Report
(4 results)
Research Products
(9 results)