李微积分

The Lie group of vertical bisections of a regular Lie groupoid

In this note we construct an infinite-dimensional Lie group structure on the group of vertical bisections of a regular Lie groupoid. We then identify the Lie algebra of this group and discuss regularity properties (in the sense of Milnor) for these Lie groups. If the groupoid is locally trivial, i.e. a gauge groupoid, the vertical bisections coincide with the gauge group of the underlying bundle. Hence the construction recovers the well known Lie group structure of the gauge groups. To establish the Lie theoretic properties of the vertical bisections of a Lie groupoid over a non-compact base, …

On fibrations of Lie groupoids

As groupoids generalize groups, motivated by group extensions we consider a kind of fibrations of Lie groupoids, called locally topological product Lie groupoid fibrations with fiber $\sf A$, i.e., \[ 1\rightarrow {\sf A} \rightarrow {\sf G} \rightarrow {\sf K}\rightarrow 1 \] where $\sf A,\sf G$ and $\sf K$ are Lie groupoids. Similar to the theory of group extensions, we show that the existence of locally topological product Lie groupoid fibrations with fiber $\sf A$ over $\sf K$ is obstructed by a groupoid cohomology of $H^3_{\bar Λ}({\sf K},Z_{\sf A})$, and these locally topological product…

李群胚的二分的李群

The Lie group of bisections of a Lie groupoid

本文赋予具有紧基的李群胚的二分群自然的局部凸李群结构。此外，我们彻底开发的连接到代数的部分相关的李代数胚，并显示了一大类李群胚，他们的团体的二分法是正规的意义上的米尔诺。

一类Baker-Campbell-Hausdorff型李群公式

Une formule de type Baker-Campbell-Hausdorff pour les groupoides de Lie

对于李群胚G，我们证明了Baker-Campbell-Hausdorff公式的一个类似公式，并计算了G的李代数胚的结构函数.

李群胚上光滑映射的可微幺半群

A differentiable monoid of smooth maps on Lie groupoids

本文研究了李群胚箭空间上的光滑映射幺半群，证明其单位群是 Milnor 意义下正则的无穷维李群，并通过推广 Stacey-Roberts 引理揭示了其与双截面群的李子群关系。

由李群胚的对分构造李群胚及其在预量子化中的应用

(Re)constructing Lie groupoids from their bisections and applications to prequantisation

本文讨论了固定紧流形上李群胚的几何与其（无限维）二分李群几何之间的关系。本文的第一部分研究了对分李群胚与给定李群胚的关系，第二部分是从对分李群的候选李群胚构造李群胚。这第二部分的程序变得可行，由于一些最近的进展，在无限维弗罗贝纽斯定理，我们大力利用。主要应用于（前）辛流形的预量子化来自于闭李子代数对闭李群的可积性约束。我们将这一约束条件的修改离散条件的期间，该流形。