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

Abstract

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 $M.$

arXiv commentCorrected version, better presentation

References in corpus (2)

• The D-topology for diffeological spaces
• An exotic zoo of diffeomorphism groups on ${\mathbb{R}}^n$

Cited by in corpus (2)

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