Research on homotopy algebraic models for geometry

几何同伦代数模型研究

• 批准号: 22740033
• 负责人: KAJIURA Hiroshige
• 金额: $ 2.58万
• 依托单位: Chiba University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22740033/
• 关键词: 幾何学; トポロジー; 代数学; 数理物理; 素粒子論

We showed that A∞-enhancements of triangulated categories are not unique in general by constructing such an example.On the other hand, for the homological mirror symmetry between symplectic manifolds and complex manifolds both of which are described by torus fibrations, we constructed noncommutative deformations of the complex manifolds, define deformations of symplectic manifolds as theire mirror partners, and discussed that homological mirror symmectry between these pairs of deformations hold true.

通过构造一个例子，证明了三角化范畴的A∞-增强在一般情况下不是唯一的.另一方面，对于环面纤维化所描述的辛流形与复流形之间的同调镜像对称，构造了复流形的非对易变形，定义辛流形的变形为它们的镜像伙伴，并讨论了这两对形变之间的同调镜像对称性成立。

项目成果

On A∞-enhancements for triangulated categories

关于三角类别的 A∞ 增强

• DOI: 10.1016/j.jpaa.2012.11.006
• 发表时间: 2013
• 期刊: Journal of Pure and Applied Algebra
• 影响因子: 0.8
• 作者: D. Alekseevsky;V. Cortes;K. Hasegawa and Y. Kamishima;Jiro Adachi;K. Moriya;Hiroshige Kajiura;足立 二郎;Hiroshige Kajiura
• 通讯作者: Hiroshige Kajiura

On the Structure of Open-Closed String Field Theory and Its Applications

论开闭弦场论的结构及其应用

• 发表时间: 2011
• 期刊: Progress of theoretical physics supplement
• 作者: 後藤四朗;大関一秀;笹木集夢;Shiro Goto and Kazuho Ozeki;笹木集夢;Hiroshige Kajiura;笹木集夢;Hiroshige Kajiura
• 通讯作者: Hiroshige Kajiura

Homologicalperturbation theory and homological mirror symmetry

同调微扰理论和同调镜像对称

• 发表时间: 2011
• 期刊: Progress inMathematics
• 作者: 後藤四朗;大関一秀;笹木集夢;Shiro Goto and Kazuho Ozeki;笹木集夢;Hiroshige Kajiura;笹木集夢;Hiroshige Kajiura;Hiroshige Kajiura
• 通讯作者: Hiroshige Kajiura