Mathematical Sciences: Symplectic Topology & Riemannian Geometry of Lagrangian Submanifolds

数学科学：辛拓扑

• 批准号: 9504455
• 负责人: Yong-Geun Oh
• 金额: $ 7.5万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504455&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Symplectic; Topology; &amp

9504455 Oh The proposed research lies in the general area of symplectic topology and geometry. More specifically, the investigator proposes to study Floer cohomology and Lagrangian submanifolds. It is expected that such a study will lead to new techniques for Lagrangian embedding and immersion problems. In addition, the investigator proposes to consider curvature estimate problems for special Lagrangian submanifolds - this may have ramifications in minimal submanifold theory. Symplectic geometry provides a rigorous mathematical setting for many problems in classical and quantum mechanics. Lagrangian submanifolds are fundamental objects - they are extremal objects in some sense - in symplectic geometry, Floer cohomology is a powerful topological tool for their study.

9504455所建议的研究属于辛拓扑和几何的一般领域。更具体地说，研究者建议研究Floer上同调和拉格朗日子流形。预计这样的研究将为拉格朗日嵌入和浸入问题带来新的技术。此外，研究者建议考虑特殊拉格朗日子流形的曲率估计问题--这可能在极小子流形理论中有分支。辛几何为经典和量子力学中的许多问题提供了严格的数学环境。拉格朗日子流形是基本对象--它们在某种意义上是极值对象--在辛几何中，Floer上同调是研究它们的一个强大的拓扑工具。