2009 Fiscal Year Final Research Report
Applications of homotopy algebras to geometry and its deformation problems
| Project/Area Number |
19740038
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Geometry
|
|---|
| 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
|
| Keywords | 幾何学 / トポロジー / 代数学 / 数理物理 / 素粒子論 |
|---|
| 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.
|
