论文标题
莫尔斯（Morse
Morse theory on Lie groupoids
论文作者
论文摘要
在本文中，我们介绍了Morse li lie classoid形态并研究其主要特性。我们表明，这个概念是莫里塔不变的，它在可区分的堆栈上产生了明确的摩尔斯功能概念。我们展示了摩尔斯引理的群体素化版本，该版本用于描述莫尔斯（Morse）lie lie closoid形态围绕其非排定临界轨道的关键亚组水平的拓扑行为。我们还证明了摩尔斯类型的不平等现象，用于某些分离的可区分堆栈并构建一个摩尔斯双复合体，其总共同体与基础lie lie类的Bott-Shulman-Stasheff同构同构。我们提供了几个示例和应用程序。
In this paper we introduce Morse Lie groupoid morphisms and study their main properties. We show that this notion is Morita invariant which gives rise to a well defined notion of Morse function on differentiable stacks. We show a groupoid version of the Morse lemma which is used to describe the topological behavior of the critical subgroupoid levels of a Morse Lie groupoid morphism around its nondegenerate critical orbits. We also prove Morse type inequalities for certain separated differentiable stacks and construct a Morse double complex whose total cohomology is isomorphic to the Bott-Shulman-Stasheff cohomology of the underlying Lie groupoid. We provide several examples and applications.
