The Lie group of bisections of a Lie groupoid

TL;DR

This paper constructs a natural Lie group structure on the bisection group of a Lie groupoid with a compact base and explores its connection to Lie algebroids, demonstrating regularity for many cases.

Contribution

It introduces a natural locally convex Lie group structure on bisections and establishes their regularity for a broad class of Lie groupoids.

Findings

Bisection groups form a natural locally convex Lie group

Connection established between bisections and Lie algebroid sections

Bisection groups are regular in Milnor's sense for many Lie groupoids

Abstract

In this article we endow the group of bisections of a Lie groupoid with compact base with a natural locally convex Lie group structure. Moreover, we develop thoroughly the connection to the algebra of sections of the associated Lie algebroid and show for a large class of Lie groupoids that their groups of bisections are regular in the sense of Milnor.