Rigidity for Poisson group actions

Abstract

In this talk we ¯rst review some classical results of rigidity for group actions of compact Lie groups on smooth manifolds and then we prove some rigidity results in the case the group action preserves a Poisson structure. The details of these proofs can be found in the paper [11] and the preprint [10]. In the general case of actions of compact Lie groups on smooth manifold there are two well-known results that entail rigidity. The ¯rst one is the theorem of Bochner [1] that says that actions of compact Lie groups can be linearized in a neighbourhood of a ¯xed point for the action. The second one is the theorem of Palais [12], that establishes that C1-close actions of compact Lie groups are conjugated via a di®eomorphism close to the identity.