Seiberg–Witten invariants

Summary

The Seiberg–Witten invariants are integer invariants of smooth closed oriented 4-manifolds, one for each spin$^c$ structure. They count solutions of the Seiberg–Witten equations, which couple a $U(1)$-connection with a spinor field through a Dirac operator. They were introduced by Edward Witten in 1994, following work of Nathan Seiberg and Witten in physics. They recover many results of Donaldson theory with much simpler analysis, because the moduli spaces are compact.