Transversality of the perturbed reduced Vafa-Witten moduli spaces on 4-manifolds

2022/12/03 by Ren Guan, Guan, Ren
Mathematics · #Geometric and Algebraic Topology #Geometry and complex manifolds #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2212.01586

Abstract

Previously we finish the establishment of the transversality of the general part of the Vafa-Witten moduli spaces, in this paper, we deal with the rest, i.e., the reduced part. We consider Vafa-Witten equation on closed, oriented and smooth Riemann 4-manifolds with C≡0, and construct perturbation to establish the transversality of the perturbed equation. Then we show that for a generic choice of the perturbation terms, the moduli space of solutions to the perturbed reduced Vafa-Witten equation for the structure group SU(2) or SO(3) on a closed 4-manifold is a smooth manifold of dimension zero.

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