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.
Domains
Differential Geometry [math.DG] General Mathematics [math.GM] Metric Geometry [math.MG] Exactly Solvable and Integrable Systems [nlin.SI] Chaotic Dynamics [nlin.CD] Pattern Formation and Solitons [nlin.PS] Mathematical Physics [math-ph] Quantum Physics [quant-ph] Library and information sciences Business administration Mathematical Physics [math-ph] Operator Algebras [math.OA] Spectral Theory [math.SP] Analysis of PDEs [math.AP]
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