Positive scalar curvature at the intersection of global analysis, geometric topology and coarse geometry

全局分析、几何拓扑和粗略几何相交处的正标量曲率

• 批准号: 43044978
• 负责人: Professor Dr. Bernhard Hanke
• 金额: --
• 依托单位: Mathematisches Institut (MI)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2007
• 资助国家: 德国
• 起止时间: 2006-12-31 至 2007-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/43044978?language=en
• 关键词: Positive; scalar; curvature; intersection; global

This project deals with the investigation of Riemannian metrics of positive scalar curvature on smooth manifolds, on manifolds with groups actions and on orbifolds. Obstructions to the existence of such metrics, and the topology of the space of positive scalar curvature metrics (if non-empty) are particular questions in this context. Special attention will be paid to the interaction of methods from differential geometry, global analysis, algebraic topology and coarse geometry. The positive scalar curvature question will also be a motivation to investigate other problems that are of interest in these specific areas, independently of the positive scalar curvature question.

本课题研究光滑流形、群作用流形和轨道流形上正标量曲率的黎曼度量。这种度量存在的障碍，以及正标量曲率度量空间的拓扑（如果非空）是这种情况下的特殊问题。课程将特别关注微分几何、全局分析、代数拓扑和粗几何方法的相互作用。正标量曲率问题也将是一个动机，去研究在这些特定领域中感兴趣的其他问题，独立于正标量曲率问题。