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

Jean-Pierre Magnot 1
  • 1 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


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.

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