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

Published online by Cambridge University Press:  13 July 2018

YUUJI TANAKA
YUUJI TANAKA*
Affiliation:
Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK e-mail: tanaka@maths.ox.ac.uk
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Abstract

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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 2 , May 2019 , pp. 471 - 486
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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