A note on symplectic topology of \(b\)-manifolds

A Poisson manifold \((M^{2n},\p)\) is \(b\)-symplectic if \(\bigwedge^n\p\) is transverse to the zero section. In this paper we apply techniques native to Symplectic Topology to address questions pertaining to \(b\)-symplectic manifolds. We provide constructions of \(b\)-symplectic structures on open manifolds by Gromov's \(h\)-principle, and of \(b\)-symplectic manifolds with a prescribed singular locus, by means of surgeries.