论文标题
可定义的子类固定的规范分层
Canonical stratification of definable Lie groupoids
论文作者
论文摘要
我们的目的是准确提出一个驯服的拓扑结构，与lie群体的规范分层。我们认为在半gebraic，亚分析，O-Minimal上的$ \ Mathbb {r} $或更一般而言，Shiota的$ \ mathfrak {x} $ - 类别。我们表明，存在一个规范的惠特尼分层，将lie群体分为可定义的地层，这些地层是在群体肌化作用下是不变的。这是对实际代数群体行动的结果的概括和完善，J。N。Mather和V. A. Vassiliev独立地说明了这一点。他们的证明的关键变化是在驯服拓扑的背景下使用Shiota的同位素论引理和近似定理。
Our aim is to precisely present a tame topology counterpart to canonical stratification of a Lie groupoid. We consider a definable Lie groupoid in semialgebraic, subanalytic, o-minimal over $\mathbb{R}$, or more generally, Shiota's $\mathfrak{X}$-category. We show that there exists a canonical Whitney stratification of the Lie groupoid into definable strata which are invariant under the groupoid action. This is a generalization and refinement of results on real algebraic group action which J. N. Mather and V. A. Vassiliev independently stated with sketchy proofs. A crucial change to their proofs is to use Shiota's isotopy lemma and approximation theorem in the context of tame topology.
