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Rigidity of actions on presymplectic manifolds

Research paper by Philippe Monnier

Indexed on: 06 Jan '16Published on: 06 Jan '16Published in: Mathematics - Symplectic Geometry



Abstract

We prove the rigidity of Hamiltonian or 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 Hamiltonian formalism associated to the presymplectic structure.