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

Author: 

Tanaka, Y

Publication Date: 

May 2019

Journal: 

GLASGOW MATHEMATICAL JOURNAL

Last Updated: 

2019-08-16T20:50:08.693+01:00

Issue: 

2

Volume: 

61

DOI: 

10.1017/S0017089518000307

page: 

471-486

abstract: 

Copyright © Glasgow Mathematical Journal Trust 2018 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.

Symplectic id: 

871237

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Submitted to ORA: 

Submitted

Publication Type: 

Journal Article