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Abstract

We introduce a cohomology theory of Koszul-Vinberg algebroids. The relationships between that cohomology and Poisson manifolds are investigated. We focus on the complex of chains of superorders [KJL1]. We prove that symbols of some sort of cycles give rise to so called bundlelike Poisson structures. In particular we show that if $E\rightarrow M$ is a transitive Koszul-Vinberg algebroid whose anchor is injective then a Koszul-Vinberg cocycle $\theta$ whose symbol has non-zero skew symmetric component defines a transversally Poissonian symplectic foliation in % $M$.