Seiberg-Witten invariants for 4-manifolds with b_+=0

Teleman, Andrei ; Okonek, Christian

HAL, hal-00881762 / Harvested from HAL

Résumé

We extend Seiberg-Witten theory to 4-manifolds with b_+=0. The moduli space of irreducible monopoles depends in this case on a parameter varying in an infinite dimensional space which is divided into a countable family of chambers by a codimension-1 wall. The Seiberg-Witten invariant associated with a class of Spin^c-structures is a functorial map which assigns an integer to every chamber and satisfies a universal wall-crossing formula for transversal wall-crossing; it should be regarded as a distinguished element in the Z-torsor of functions satisfying the wall-crossing formula. The Seiberg-Witten invariant for a 3-manifold with b_1=0 is completely determined by the 4-dimensional invariant of the product with a circle. When the base manifold is a complex surface, a Kobayashi-Hitchin-type correspondence allows us to compute the invariants in the so-called complex geometric chambers by counting complex curves.

Détail

Publié le : 2000-07-05
Classification:  Seiberg-Witten invariants,  Inoue surfaces,  Hopf surfaces,  MSC 53 C, 32 C10, 32 L05, 32 L10, 57R57,  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG],  [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT],  [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]