Mathematical Sciences: Differential Structures

数学科学：微分结构

• 批准号: 9504913
• 负责人: Eugenio Calabi
• 金额: $ 55万
• 依托单位: University of Pennsylvania
• 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: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504913&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Differential; Structures

9504913 Calabi The proposed research involves various aspects of differential geometry and differential topology: variational problems in surface theory, knot theory in the presence of curvature, topological classification of representations, homology manifolds, Einstein metrics on homogeneous spaces, equivariant K-theory, and Poisson manifolds are among the topics proposed. Differential geometry studies shapes in space keeping in mind their distance and curvature properties; differential topology concentrates on relative positions in space whilst ignoring distance or curvature. This group proposal then seeks to establish a connection between these two areas of research by asking such questions as how the topology of a space determines its geometry.

小行星9504913 拟议的研究涉及微分几何和微分拓扑学的各个方面：变分问题的曲面理论，结理论的存在曲率，拓扑分类的表示，同源流形，爱因斯坦度量齐次空间，等变K理论，泊松流形是其中提出的主题。 微分几何研究空间中的形状，同时记住它们的距离和曲率属性;微分拓扑学集中在空间中的相对位置，而忽略距离或曲率。这个小组的建议，然后试图建立这两个研究领域之间的联系，提出这样的问题，如空间的拓扑结构如何决定其几何形状。