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In mathematics, Seiberg–Witten invariants are invariants of compact smooth 4-manifolds introduced by , using the Seiberg–Witten theory studied by during their investigations of Seiberg–Witten gauge theory. Seiberg–Witten invariants are similar to Donaldson invariants and can be used to prove similar (but sometimes slightly stronger) results about smooth 4-manifolds. They are technically much easier to work with than Donaldson invariants; for example, the moduli spaces of solutions of the Seiberg–Witten equations tend to be compact, so one avoids the hard problems involved in compactifying the moduli spaces in Donaldson theory. For detailed descriptions of Seiberg–Witten invariants see , , , , . For the relation to symplectic manifolds and Gromov–Witten invariants see . For the early history see . ==Spin''c''-structures== The Seiberg-Witten equations depend on the choice of a complex spin structure, Spin''c'', on a 4-manifold ''M''. In 4 dimensions the group Spin''c'' is :(''U''(1)×Spin(4))/(Z/2Z), and there is a homomorphism from it to SO(4). A Spin''c''-structure on ''M'' is a lift of the natural SO(4) structure on the tangent bundle (given by the Riemannian metric and orientation) to the group Spin''c''. Every smooth compact 4-manifold ''M'' has Spin''c''-structures (though most do not have spin structures). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Seiberg–Witten invariant」の詳細全文を読む スポンサード リンク
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