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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