Smooth Lie groups actions are diffeological subgroups
November 16, 2010, update June 17, 2011
In this paper, in collaboration with Yael Karshon, we prove that a smooth monomorphism from a Lie group G into the group Diff(M), where M is a manifold, is necessarily an induction. The group G and the manifold M are assumed to be second countable. This is the answer to a Yael question: make intrinsic the usual concept of “Lie subgroup” of group of diffeomorphisms, defined by smooth actions of Lie groups on manifolds. Concept she uses intensively in her work on symplectic geometry. (Final version)

Proceedings of the American Mathematical Society, 140 (2012), 731-739.