A Morse Theoretical Approach to the Seiberg-witten Functional
نویسنده
چکیده
In the Theory of the Seiberg-Witten Equations, the configuration space is Cα = Aα × Γ (S + α ), where Aα is a space of u1-connections and Γ (S + α ) is the space of sections of the complex spinor bundle over X. Since the SWequation fits in a variational approach, invariant by the action of the Gauge Group Gα = Map(X,U1), which satisfies the Palais-Smale Condition, our aim is to obtain existence of solutions to the 2-order SW-equations by describing the weak homotopy type of the space Aα ×Gα Γ (S + α ). The 2 -order SWequations are the Euler-Lagrange equation of a functional, they generalise the 1-order SW-equations
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