On the Existence of Global Bisections of Lie Groupoids

TL;DR

This paper proves that every source connected Lie groupoid admits global bisections through any point, which can be constructed as exponentials close to a given curve, with applications discussed.

Contribution

It establishes the existence of global bisections in source connected Lie groupoids and provides a method to construct them as exponentials near a prescribed curve.

Findings

Existence of global bisections through any point in source connected Lie groupoids

Construction of bisections as exponentials close to a given curve

Applications of these bisection existence results

Abstract

We show that every source connected Lie groupoid always has global bisections through any given point. This bisection can be chosen to be the multiplication of some exponentials as close as possible to a prescribed curve. The existence of bisections through more than one prescribed points is also discussed. We give some interesting applications of these results.