A new construction of Poisson manifolds (Q1883975)

One of the main results of the paper under review (namely, theorem~2) is that, for every finitely presentable group \(G\) and arbitrary integers \(n\), \(d\), with \(4\leq d\leq n\) and \(d\) even, there exists a closed orientable Poisson manifold \(M\) of dimension \(n\) and constant rank \(d\) such that the fundamental group of \(M\) is isomorphic to \(G\). The proof is accomplished by developing certain surgery techniques of construction of Poisson manifolds. These techniques are inspired by those of \textit{R. E. Gompf} [Ann. Math. (2) 142, No. 3, 527--595 (1995; Zbl 0849.53027)].