论文标题
跨性别差异几何学的类固醇方法
A groupoid approach to transitive differential geometry
论文作者
论文摘要
这项工作是一个正在进行的计划的衍生产品，旨在重新审视现代角度的原始研究对伪群和几何结构的原始研究。我们编码由瞬态谎言伪集团诱导的几何结构中的几何结构中，配备了由$ \ mathfrak {g} $的sibergebra生成的横向平行叶片，称为cartan捆绑包。我们的方法与Arxiv：1911.13147相辅相成，是基于lie lie clopoids的莫里塔等效性。在确定了主要的示例和属性之后，我们就lie代数形成了平坦的概念，该代数涵盖了$ g $结构的经典整合性，cartan几何形状的平坦度以及接触结构的整合性。
This work is a spin-off of an on-going programme which aims at revisiting the original studies of Lie and Cartan on pseudogroups and geometric structures from a modern perspective. We encode geometric structures induced by transitive Lie pseudogroups into principal $G$-bundles equipped with a transversally parallelisable foliation generated by a subalgebra of $\mathfrak{g}$, called Cartan bundles. Our approach is complementary to arXiv:1911.13147 and is based on Morita equivalence of Lie groupoids. After identifying the main examples and properties, we develop a notion of flatness with respect to a Lie algebra, which encompasses the classical integrability of $G$-structures, the flatness of Cartan geometries, as well as the integrability of contact structures.
