• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.593-601
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• 2003

Let X be a 4-manifold obtained by gluing two symplectic 4-manifolds Xi, i = 1, 2, along embedded surfaces. Using the gradient flow of a functional on 3-dimensional Seiberg-Witten theory along the cylindrical end, we study the Seiberg-Witten equations on X and have a product formula of Seiberg-Witten invariants on X from the ones on Xi, i = 1, 2.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1183-1197
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• 2006

Let X be a smooth, closed, connected spin 4-manifold with $b_1(X)=0$ and signature ${\sigma}-(X)$. In this paper we use Seiberg-Witten theory to prove that if X admits a spin alternating $A_4$ action, then $b^+_2(X)$ ${\geq}$ |${\sigma}{(X)}$|/8+3 under some non-degeneracy conditions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.3
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• pp.205-216
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• 2012

When it comes to Lorentz symmetry violation, there are generally two approaches to studying noncommutative field theory: 1) conventional fields are equivalent to noncommutative fields; however, symmetry groups are larger. 2) The symmetry group is the same as conventional standard model's symmetry group; but fields here are written based on the Seiberg-Witten map. Here by adopting the first approach, we aim to connect Lorentz violation coefficients with noncommutative parameters and compare the results with the second approach's results. Through the experimental values obtained for the Lorentz-violating parameters, we obtain a limit of noncommutative symmetry.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.683-691
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• 1999

It has long been a question which homology class is represented by an embedded 2-sphere in a smooth 4-manifold. In this article we study the adjunction inequality, one of main results of Seiberg-Witten theory in smooth 4-manifolds, for an embedded 2-sphere. As a result, we give a criterion which homology class cannot be represented by an embedded 2-sphere in some cases.