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

黎曼流形的分层以各种方式出现。层化流形上的整体结构和不变量与层化所给出子对象上相应的结构和不变量之间存在着很强的相互作用。我们的目标是将这种相互作用用于选定的两个方向上或甚至两个方向上具有非负截面曲率的空间：有时适当的分层是解决分层空间全局问题的关键。有时黎曼流形的整体问题在本质上被考虑时很难回答，但当人们采用某种环境结构时，它可能会变得可解。问题总是在于找到合适的分层。为了做到这一点，我们详细地研究了大量的分层。

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.