Seminários de Geometria 24 de Julho 2008, 14h00 Abstract: We discuss the variational calculus for the Faddeev-Hopf model on a Riemannian manifold, with Kaehler, or even symplectic, target space, in the strong coupling limit. This model has interesting similarities with pure Yang-Mills theory, namely conformal invariance in dimension 4 and an infinite dimensional symmetry group. We calculate the first and second variation formulae for this functional and discuss some solutions and their stability properties. In particular, it is proved that all immersive solutions are minimizing in their homotopy class. From an explicit description of the spectral behaviour of the Hopf map $S^3\to S^2$, we are able to prove a conjecture of Ward concerning the stability of this map in the full Faddeev-Hopf model. | back |