论文标题
差异莫里塔等效
Diffeological Morita Equivalence
论文作者
论文摘要
我们引入了一种新的莫里塔等效概念，即差异类固醇，从而概括了lie gropsoid的原始概念。为此，我们开发了一种差异群体，捆绑和 - 验证的理论。我们为这些捆绑包定义了公国的概念，该束使用俯冲的概念，概括了谎言群体（OID）主束的概念。我们说，只有当它们之间存在双骨bi骨时，两种差异群是莫里塔当量的。使用Hilsum-skandalis张量产物，我们进一步定义了差异的组成，并获得了生物差异。我们的主要结果是以下内容：仅当该生物中的Bibundle是双尺度的，并且仅当它在此生物中弱可逆。这概括了lie群体理论中众所周知的定理。作为框架的应用，我们证明了两个莫里塔等效分组的轨道空间是差异的。我们还表明，不同差异类固醇的特性及其动作类别是莫里塔不变的。
We introduce a new notion of Morita equivalence for diffeological groupoids, generalising the original notion for Lie groupoids. For this we develop a theory of diffeological groupoid actions, -bundles and -bibundles. We define a notion of principality for these bundles, which uses the notion of a subduction, generalising the notion of a Lie group(oid) principal bundle. We say two diffeological groupoids are Morita equivalent if and only if there exists a biprincipal bibundle between them. Using a Hilsum-Skandalis tensor product, we further define a composition of diffeological bibundles, and obtain a bicategory DiffBiBund. Our main result is the following: a bibundle is biprincipal if and only if it is weakly invertible in this bicategory. This generalises a well known theorem from the Lie groupoid theory. As an application of the framework, we prove that the orbit spaces of two Morita equivalent diffeological groupoids are diffeomorphic. We also show that the property of a diffeological groupoid to be fibrating, and its category of actions, are Morita invariants.
