Rigidity of actions on presymplectic manifolds
Symplectic Geometry
2017-04-25 v3 Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1601.01217,
title = {Rigidity of actions on presymplectic manifolds},
author = {Philippe Monnier},
journal= {arXiv preprint arXiv:1601.01217},
year = {2017}
}
Comments
There is an important mistake in the definition of the global smoothing operator preserving the presymplectic form