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A normal form theorem around symplectic leaves. (English) Zbl 1262.53078

This paper gives a generalization of Conn’s linearization theorem. Let us recall that when \(M\) is a Poisson manifold, the flows of the Hamiltonian vector fields give a partition of \(M\) into symplectic leaves. In this work, the authors prove a normal form theorem around symplectic leaves. To achieve their aim, they use the Poisson homology bundle associated to a leaf and homotopy theory. They finally obtain a geometric version of the local Reeb stability from foliation theory and of the slice theorem from group actions.

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids
53C12 Foliations (differential geometric aspects)
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