Poisson Cohomology

Abstract

The subject of this chapter is related to that of the previous one in an obvious way. Just as the usual calculus on manifolds leads to the de Rham cohomology, the Poisson calculus leads to the Lichnerowicz-Poisson cohomology first studied in [Lh2]. These new cohomology spaces are far from being as interrelated with the topology of the manifold as the de Rham spaces are, and, moreover, they are “too big”, and their actual computation is both more complicated and less significant than in the case of the de Rham cohomology. However, they are interesting because they allow us to describe various results concerning Poisson structures, in particular, one important result about the quantization of the manifold