Spectral Invariants in Geometry and Topology

几何和拓扑中的谱不变量

• 批准号: 9704633
• 负责人: John Lott
• 金额: $ 8.03万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-06-01 至 2001-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704633&HistoricalAwards=false
• 关键词: Spectral; Invariants; Geometry; Topology

9704633 Lott This project is concerned with relationships between geometric analysis and the topology of manifolds. Among the topics to be pursued are: L2-invariants of covering spaces and their possible extensions; p-form eigenvalues of collapsing Riemannian manifolds and about topological obstructions to collapse; analytic torsion forms and the topology of diffeomorphism groups. Manifolds are curved spaces generalizing surfaces in space. Thus an important geometric property of a manifold is its curvature, which is defined locally. It turns out that there are restrictions on the overall shape of the manifold, i.e., its topology, for the manifold to be able to carry certain types of curvatures; conversely, knowing the curvature one can make certain predictions about its global shape.

9704633洛特这个项目是关于几何分析和流形拓扑之间的关系。要讨论的主题包括：覆盖空间的l2不变量及其可能的扩展；坍缩黎曼流形的p型特征值及其拓扑障碍解析扭转形式与微分同构群的拓扑结构。流形是曲面在空间中的广义化。因此流形的一个重要几何性质是它的曲率，它是局部定义的。事实证明流形的整体形状是有限制的，也就是它的拓扑结构，使得流形能够携带某些类型的曲率；相反，知道了曲率，就可以对它的整体形状做出一定的预测。