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High Quality Content by WIKIPEDIA articles! In mathematics, Seiberg Witten invariants are invariants of compact smooth 4-manifolds introduced by Witten (1994), using the Seiberg-Witten theory studied by Seiberg and Witten (1994a, 1994b) 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 (Donaldson 1996), (Moore 2001), (Morgan 1996), (Nicolaescu 2000), (Scorpan 2005, Chapter 10). For the relation to symplectic manifolds and Gromov-Witten invariants see (Taubes 2000). For the early history see (Jackson 1995).