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Demonstratio Mathematica

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Volume 51, Issue 1


The group of diffeomorphisms of a non-compact manifold is not regular

Jean-Pierre Magnot
  • LAREMA - UMR CNRS 6093, Université d’Angers, 2 Boulevard Lavoisier - 49045 Angers cedex 01 and Lycée Jeanne d’Arc, Avenue de grande bretagne, F-63000 Clermont-Ferrand, France
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Published Online: 2018-03-01 | DOI: https://doi.org/10.1515/dema-2018-0001


We show that a group of diffeomorphisms D on the open unit interval I, equipped with the topology of uniform convergence on any compact set of the derivatives at any order, is non-regular: the exponential map is not defined for some path of the Lie algebra. This result extends to the group of diffeomorphisms of finite dimensional, non-compact manifold M.

Keywords: diffeology; diffeomorphisms; infinite dimensional Lie groups; exponential map

MSC 2010: 22E65; 22E66


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About the article

Received: 2017-05-24

Accepted: 2017-12-21

Published Online: 2018-03-01

Citation Information: Demonstratio Mathematica, Volume 51, Issue 1, Pages 8–16, ISSN (Online) 2391-4661, DOI: https://doi.org/10.1515/dema-2018-0001.

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© 2018 Jean-Pierre Magnot. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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