The group of diffeomorphisms of a non-compact manifold is not regular. (English) Zbl 1387.22019
Summary: We show that a group of diffeomorphisms \(\mathcal{D}\) 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 a finite dimensional, non-compact manifold \(M\).
MSC:
| 22E65 | Infinite-dimensional Lie groups and their Lie algebras: general properties |
| 22E66 | Analysis on and representations of infinite-dimensional Lie groups |
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