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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.
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https://hal.archives-ouvertes.fr/hal-01831632
Contributor : Jean-Pierre Magnot <>
Submitted on : Friday, July 6, 2018 - 9:51:50 AM
Last modification on : Monday, March 9, 2020 - 6:15:59 PM
Document(s) archivé(s) le : Tuesday, October 2, 2018 - 4:43:10 AM

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Jean-Pierre Magnot. The group of diffeomorphisms of a non-compact manifold is not regular. Demonstratio Mathematica, De Gruyter, 2018, 51 (1), pp.8 - 16. ⟨10.1515/dema-2018-0001⟩. ⟨hal-01831632⟩

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