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

Magnot J.-P.

Demonstratio Mathematica

2018

Vol. 51, nr 1

8--16

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.