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arXiv · 1208.2297

Rigidity around Poisson Submanifolds

Ioan Marcut
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Abstract

We prove a rigidity theorem in Poisson geometry around compact Poisson submanifolds, using the Nash-Moser fast convergence method. In the case of one-point submanifolds (fixed points), this immediately implies a stronger version of Conn's linearization theorem, also proving that Conn's theorem is, indeed, just a manifestation of a rigidity phenomenon; similarly, in the case of arbitrary symplectic leaves, it gives a stronger version of the local normal form theorem; another interesting case corresponds to spheres inside duals of compact semisimple Lie algebras, our result can be used to fully compute the resulting Poisson moduli space.

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Ioan Marcut. 2012-08-10. Rigidity around Poisson Submanifolds. https://doi.org/10.1007/s11511-014-0118-1

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