Stratifications of spaces with nonnegative sectional curvature and their relation to global structures and invariants

具有非负截面曲率的空间分层及其与整体结构和不变量的关系

• 批准号: 5406874
• 负责人: Professor Dr. Uwe Abresch
• 金额: --
• 依托单位: Lehrstuhl Analysis, insbes. Differentialgeometrie und Dynamische Systeme
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2003
• 资助国家: 德国
• 起止时间: 2002-12-31 至 2008-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5406874?language=en
• 关键词: Stratifications; spaces; nonnegative; sectional; curvature

Stratifications of Riemannian manifolds arise in various ways. There is a strong interplay between the global structures and invariants on the stratified manifold and the corresponding structures and invariants on subobjects given by the stratification. Our goal is to use this interaction for selected spaces of nonnegative sectional curvature in either of the two or even in both directions depending on the situation: Somtimes a suitable stratification is the key to solve a global question for the stratified space. Sometimes a global question for a Riemannian manifold is hard to answer when it is considered intrinsically, but it may become solvable when one employs a certain ambient structure. The problem always is to find appropriate stratifications. In order to do this we study a large amount of stratifications in detail.

黎曼流形的分层以各种方式出现。分层流形上的整体结构和不变量与分层所给出的子流形上的相应结构和不变量之间存在着很强的相互作用。我们的目标是使用这种相互作用的选择空间的非负截面曲率的两个或甚至在两个方向上取决于情况：有时一个合适的分层是解决一个全球性问题的分层空间的关键。有时，黎曼流形的整体问题在本质上是很难回答的，但当我们使用某种环境结构时，它可能是可解的。问题总是要找到适当的分层。为了做到这一点，我们详细研究了大量的分层。