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arXiv · 1410.1691

A perturbation and generic smoothness of the Vafa-Witten moduli spaces on closed symplectic four-manifolds

Yuuji Tanaka
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Abstract

We prove a Freed-Uhlenbeck style generic smoothness theorem for the moduli space of solutions to the Vafa--Witten equations on a closed symplectic four-manifold by using a method developed by Feehan for the study of the $PU(2)$-monopole equations on smooth closed four-manifolds. We introduce a set of perturbation terms to the Vafa--Witten equations, and prove that the moduli space of solutions to the perturbed Vafa-Witten equations on a closed symplectic four-manifold for the structure group $SU(2)$ or $SO(3)$ is a smooth manifold of dimension zero for a generic choice of the perturbation parameters.

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Yuuji Tanaka. 2014-10-07. A perturbation and generic smoothness of the Vafa-Witten moduli spaces on closed symplectic four-manifolds. https://doi.org/10.1017/s0017089518000307

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