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A PERTURBATION AND GENERIC SMOOTHNESS OF THE VAFA–WITTEN MODULI SPACES ON CLOSED SYMPLECTIC FOUR-MANIFOLDS

  • YUUJI TANAKA (a1)

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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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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