The Lie group of bisections of a Lie groupoid

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.

31 pages, LaTex, v2: corrected several typos and added some remarks, the main results remain unchanged

References in corpus (4)

• Differential cohomology in a cohesive infinity-topos
• Lie Group Structures on Symmetry Groups of Principal Bundles
• The Lie algebra of the group of bisections
• Differentiable vectors and unitary representations of Frechet-Lie supergroups

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