An openness theorem for harmonic $2$-forms on $4$-manifolds

Abstract

Let $M$ be a closed, oriented $4$-manifold with $b^{\pm}_{2} \gt 0$. In this paper we show that the space of transverse intrinsically harmonic $2$-forms in a fixed cohomology class is open in the space of closed $2$-forms, subject to a condition which arises from cohomological considerations of a singular differential ideal.