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In mathematics, and especially gauge theory, Seiberg–Witten invariants are invariants of compact smooth oriented 4-manifolds introduced by Edward Witten, using the Seiberg–Witten theory studied by Nathan Seiberg and Witten during their investigations of Seiberg–Witten gauge 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.