Rigidity of Hamiltonian ations on Poisson manifolds (2012)

(with E Miranda and Ph Monnier) Rigidity of Hamiltonian ations on Poisson manifolds , Advances in Mathematics, Volume 229, Issue 2, 30 January 2012, Pages 1136-1179

Arxiv: http://arxiv.org/abs/1102.0175

ScienceDirect: http://www.sciencedirect.com/science/article/pii/S0001870811003574

It took us several years to write up this paper, because although we “always knew” that the rigidity result was true for Hamiltonian actions of compact semi-simple Lie groups on Poisson manifolds, the proof was a bit too technical. We tried to make the proof look as simple as possible, and  established an abstract Nash-Moser smooth normal form theorem as a machinary to use in these kinds of situations. Hopefully, our abstract normal form theorem will fnd many other applications besides this rigidity of Hamiltonian actions.

Cited in:

1. # Michael Bailey, Local classification of generalized complex structures, preprint arxiv 1201.4887 (2012)
2. R Flores-Espinoza, Perturbations of Collective Hamiltonian Systems generated by Lie Algebra contractions, J. Phys.: Conf. Ser. 343 (2012)