On the general part of the perturbed Vafa-Witten moduli spaces on 4-manifolds

Abstract

In this paper we consider the Vafa-Witten equations on closed, oriented and smooth 4-manifolds, and construct a set of perturbation terms to establish the transversality of the perturbed Vafa-Witten equations at the general part of the solutions. Then we show that for a generic choice of the perturbation terms, this part of the moduli space for the structure group $SU(2)$ or $SO(3)$ on a closed 4-manifold is a smooth manifold of dimension zero.