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.
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
It is shown that the identity component of the group of al compac tly suported C infinity -diffeomorphisms of a manifold with corners is perfect provided the manifold has no vertices. An analogous result for Cr -diffeomorphism still holds whenever r > n+1, wheren is the dimension of the manifold. These results constiute a generalization of a well-known theorem by Thurston and Mather on the simplicity of diffeomorphism groups of boundaryless manifolds.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.