Analysis of the Faddeev model

Abstract

In this paper we consider a generalization of the Faddeev model for the maps from a closed three-manifold into the two-sphere. We give a novel representation of smooth $S^2$-valued maps based on flat connections. This representation allows us to obtain an analytic description of the homotopy classes of $S^2$-valued maps that generalizes to Sobolev maps. It also leads to a new proof an old theorem of Pontrjagin. For the generalized Faddeev model, we prove the existence of minimizers in every homotopy class.

References in corpus (1)

• Knots and Particles

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