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arXiv · 1011.5998

Formal equivalence of Poisson structures around Poisson submanifolds

Ioan Marcut
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Abstract

Let (M, π ) be a Poisson manifold. A Poisson submanifold $P \in M$ gives rise to an algebroid $AP \rightarrow P$, to which we associate certain chomology groups which control formal deformations of π around P . Assuming that these groups vanish, we prove that π is formally rigid around P , i.e. any other Poisson structure on M , with the same first order jet along P as π is formally Poisson diffeomorphic to π . When P is a symplectic leaf, we find a list of criteria which imply that these cohomological obstructions vanish. In particular we obtain a formal version of the normal form theorem for Poisson manifolds around symplectic leaves.

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Ioan Marcut. 2010-11-27. Formal equivalence of Poisson structures around Poisson submanifolds. https://arxiv.org/abs/1011.5998

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