论文标题
乘法Ehresmann连接
Multiplicative Ehresmann connections
论文作者
论文摘要
我们发展了涵盖身份及其无穷小对应物的二种二团淹没的乘法Ehresmann连接的理论。我们构建了这种连接存在的障碍，我们证明了几类有趣类的lie类和谎言代数的障碍物，包括所有适当的lie groupoids。我们表明，主要捆绑联系理论中的许多概念在此一般设置中具有类似物，包括连接1形，曲率2形式，比安奇身份等。在[17]中，我们提供了此处获得的结果的非平凡应用，以在Poisson几何形状中构建本地模型，并在Poisson submanifolds周围获得线性化的结果。
We develop the theory of multiplicative Ehresmann connections for Lie groupoid submersions covering the identity, as well as their infinitesimal counterparts. We construct obstructions to the existence of such connections, and we prove existence for several interesting classes of Lie groupoids and Lie algebroids, including all proper Lie groupoids. We show that many notions from the theory of principal bundle connections have analogues in this general setup, including connections 1-forms, curvature 2-forms, Bianchi identity, etc. In [17] we provide a non-trivial application of the results obtained here to construct local models in Poisson geometry and to obtain linearization results around Poisson submanifolds.
