The topology of symplectic manifolds (Q2719817)

The author studies symplectic manifolds as purely topological objects. He provides an informal introduction to symplectic structures from a topological viewpoint, discusses obstructions to the existence of symplectic structures and provides their topological construction basing on \(J\)-holomorphic maps. He shows that the construction is universal and realizing a dense subset of all symplectic structures on any given manifold. The main result of the paper is to show that a deformation class of hyperpencils uniquely determines an isotopy class of symplectic forms and this isotopy class is characterized as being the unique class containing representatives \(\omega\) for which \([\omega]=f^*h \in H^2_{dR}(X)\) and \(\omega\) tames a given hyperpencil in the deformation class.