Seiberg-Witten invariants and real curves

Damien Gayet (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

On a compact oriented four-manifold with an orientation preserving involution c, we count solutions of Seiberg-Witten equations, which are moreover symmetrical in relation to c, to construct "real" Seiberg-Witten invariants. Using Taubes' results, we prove that on a symplectic almost complex manifold with an antisymplectic and antiholomorphic involution, this invariants are not all trivial, and that the canonical bundle is represented by a real holomorphic curve.

Domaines: Géométrie différentielle [math.DG]; Géométrie symplectique [math.SG]; Variables complexes [math.CV]

Damien Gayet. Seiberg-Witten invariants and real curves. 2004. ⟨hal-00001505⟩