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Journal Articles Demonstratio Mathematica Year : 2018

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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Dates and versions

hal-01831632 , version 1 (06-07-2018)

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