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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. MSC(2010): 22E65; 22E66.
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Dates and versions

hal-01653814 , version 1 (01-12-2017)

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  • HAL Id : hal-01653814 , version 1

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Jean-Pierre Magnot. THE GROUP OF DIFFEOMORPHISMS OF A NON COMPACT MANIFOLD IS NOT REGULAR. 2017. ⟨hal-01653814⟩
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