Spectral Invariants in Geometry and Topology

9704633 Lott这个项目涉及几何分析和流形拓扑之间的关系。其中要研究的主题包括：覆盖空间的L2-不变量及其可能的扩张；关于折叠黎曼流形和关于折叠的拓扑障碍的p型特征值；解析扭转形式和微分同胚群的拓扑。流形是空间中曲面的泛化。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，即它的拓扑结构，对于流形能够承载某些类型的曲率是有限制的；相反，知道曲率就可以对它的全局形状做出某些预测。

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.