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Annals of Global Analysis and Geometry

, Volume 48, Issue 1, pp 87–123 | Cite as

The Lie group of bisections of a Lie groupoid

  • Alexander Schmeding
  • Christoph Wockel
Article

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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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.NTNU TrondheimTrondheimNorway
  2. 2.University of HamburgHamburgGermany

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