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 S2-valued maps based on flat connections. This representation allows us to obtain an analytic description of the homotopy classes of S2-valued maps that generalizes to Sobolev maps. It also leads to a new proof of an old theorem of Pontrjagin. For the generalized Faddeev model, we prove the existence of minimizers in every homotopy class.
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Communicated by L. Takhtajan
The first author was partially supported by NSF grant DMS-0204651
The second author was partially supported by NSF grant DMS-0436403
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Auckly, D., Kapitanski, L. Analysis of S2-Valued Maps and Faddeev’s Model. Commun. Math. Phys. 256, 611–620 (2005). https://doi.org/10.1007/s00220-005-1289-6
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DOI: https://doi.org/10.1007/s00220-005-1289-6