Poisson Equivalence over a Symplectic Leaf

Details Poisson Equivalence over a Symplectic Leaf Poisson Equivalence over a Symplectic Leaf

2005-03-28

arxiv.org/abs/math/0503628v2

Mathematics

Symplectic Geometry

Latex file, 52p, minor corrections

Scientific paper

We study the equivalence of Poisson structures around a given symplectic leaf of nonzero dimension. Some criteria of Poisson equivalence are derived from a homotopy argument for coupling Poisson structures. In the case when the transverse Lie algebra of the symplectic leaf is semisimple of compact type, we show that an obstruction to the linearizability is the cohomology class of a Casimir 2-cocycle. This allows us to obtain a semilocal analog of the Conn linearization theorem and to clarify examples of nonlinearizable Poisson structures due to \cite{DW}.

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