A proof of a theorem of Luttinger and Simpson about the number of vanishing circles of a near-symplectic form on a 4-dimensional manifold (Q2471523)

A near symplectic form on a four dimensional manifold is a nontrivial closed form whose square is non-negative and, on its zero locus, has rank 3 derivative. The main result of the paper is the proof of the following result announced by Luttinger and Simpson: Let \(n\) be a positive integer. A smooth, oriented, compact, connected four manifold that admits a near symplectic form in a given cohomology class admits one in the same class whose zero locus consists of the disjoint union of \(n\) embedded circles. The author also proves a version of the above result for asymptotically Euclidean manifolds.