Rigidity of actions on presymplectic manifolds

We prove the rigidity of presymplectic actions of a compact semisimple Lie algebra on a presymplectic manifold of constant rank in the local and global case. The proof uses an abstract normal form theorem we had stated in a previous work, based on an iterative process of Nash-Moser type. In order to use correctly this abstract theorem, we need to construct a new smoothing operator for differential forms and multivector fields which preserves the presymplectic feature.