# The Lie group of bisections of a Lie groupoid

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## 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.

## Keywords

Global analysis Lie groupoid Infinite-dimensional Lie group Mapping space Local addition Bisection Regularity of Lie groups## Mathematics Subject Classification

Primary: 22E65 Secondary: 58H05 46T10 58D05## Notes

### Acknowledgments

The research on this paper was partially supported by the DFG Research Training group 1670 *Mathematics inspired by String Theory and Quantum Field Theory*, the Scientific Network *String Geometry* (DFG project code NI 1458/1-1) and the project *Topology in Norway* (Norwegian Research Council project 213458).

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