A NEW CONSTRUCTION OF POISSON MANIFOLDS

Abstract

A new technique is presented for construction of Poisson manifolds. This technique is inspired by surgery ideas used to define Poisson structures on 3-manifolds and Gompf's surgery construction for symplectic manifolds. As an application of these ideas it is proved that for all n ≥ d ≥ 4, d even, any finitely presentable group is the fundamental group of a n-dimensional orientable closed Poisson manifold of constant rank d. The unimodularity of some of the Poisson structures thus constructed is studied.