Rigidity of Hamiltonian actions

Finally (after several years of dragging our feet), my colleagues Eva Miranda and Philippe Monnier and I have just finished our paper on the rigidity of Hamiltonian actions of compact semisimple Lie groups on Poisson manifolds.

The rigidity phenomenon here is quite natural. It has been  known for a long time that compact group actions are rigid (i.e. any two nearby actions are isotopic). However, in the context of compact group actions which preserve an additional structure, the problem  can become very difficult. In the Poisson case, the difficulty comes from the fact that the path method doesn’t work (i.e. given two nearby Poisson structures a-priori there is no natural way to connect them by a path of Poisson structures). Our proof of rigidity uses the so-called Nash-Moser normal form theorem (which we first developed for another problem of smooth normal forms of Poisson structures).

Our paper, entitled “Rigidity of Hamiltonian group actions on Poisson manifolds”, has been sent to Arxiv, and also to a good journal. It can also be downloaded from here: Rigidity.

How I can celebrate the New Year of the Cat & the Rabbit with this new paper :D

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