论文标题
li lie clopoids和chern-weil理论的联系
Connections on Lie groupoids and Chern-Weil theory
论文作者
论文摘要
令$ \ mathbb {x} = [x_1 \ rightrightArrows x_0] $为配备连接的lie groupoid，由平滑分布$ \ mathcal {h} \ subset t x_1 $ transeversal to to s fibers fibers to s offence Map的纤维。在假设分布$ \ mathcal {h} $是可集成的假设之后，我们定义了$ $（\ Mathbb {x}，\ Mathcal {h}）$的De Rham同谋的版本，我们研究了$ g $ bundles over $ g $ bundles $（\ mathbb {x Mathi at y Mathie）的contermant of conteriagy of（\ mathbb {x}向量束。我们还讨论了可区分堆栈的相关结构。最后，我们开发了相应的Chern-Weil理论，并描述了主G型束的特征类别，该类别是一对$（\ Mathbb {x}，\ Mathcal {H}）$。
Let $\mathbb{X}=[X_1\rightrightarrows X_0]$ be a Lie groupoid equipped with a connection, given by a smooth distribution $\mathcal{H} \subset T X_1$ transversal to the fibers of the source map. Under the assumption that the distribution $\mathcal{H}$is integrable, we define a version of de Rham cohomology for the pair $(\mathbb{X}, \mathcal{H})$, and we study connections on principal $G$-bundles over $(\mathbb{X}, \mathcal{H})$ in terms of the associated Atiyah sequence of vector bundles. We also discuss associated constructions for differentiable stacks. Finally, we develop the corresponding Chern-Weil theory and describe characteristic classes of principal G-bundles over a pair $(\mathbb{X}, \mathcal{H})$.
