Journal of Symplectic Geometry

Volume 2 (2004)

Number 1

A NEW CONSTRUCTION OF POISSON MANIFOLDS

Pages: 83 – 107

DOI: http://dx.doi.org/10.4310/JSG.2004.v2.n1.a3

Authors

A. Ibort

D. Martínez Torres

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.

Full Text (PDF format)