The perturbation of the Seiberg-Witten equations revisited

We introduce a new class of perturbations of the Seiberg-Witten equations. Our perturbations offer flexibility in the way the Seiberg-Witten invariants are constructed and also shed a new light to LeBrun's curvature inequalities.Comment: typos correcte

Nilpotency of the Bauer-Furuta stable homotopy Seiberg-Witten invariants

We prove a nilpotency theorem for the Bauer-Furuta stable homotopy Seiberg-Witten invariants for smooth closed 4-manifolds with trivial first Betti number.Comment: This is the version published by Geometry & Topology Monographs on 29 January 200

Homotopy theoretical considerations of the Bauer-Furuta stable homotopy Seiberg-Witten invariants

We show the "non-existence" results are essential for all the previous known applications of the Bauer-Furuta stable homotopy Seiberg-Witten invariants. As an example, we present a unified proof of the adjunction inequalities. We also show that the nilpotency phenomenon explains why the Bauer-Furuta stable homotopy Seiberg-Witten invariants are not enough to prove 11/8-conjecture.Comment: This is the version published by Geometry & Topology Monographs on 29 January 200